1322:
479:
114:
342:
420:
699:
1421:, the second derivative of the free energy with the field, changes discontinuously. Under the Ehrenfest classification scheme, there could in principle be third, fourth, and higher-order phase transitions. For example, the Gross–Witten–Wadia phase transition in 2-d lattice quantum chromodynamics is a third-order phase transition. The Curie points of many ferromagnetics is also a third-order transition, as shown by their specific heat having a sudden change in slope.
1335:
5178:
33:
1636:
magnetic phases coexisting, down to the lowest temperature. First reported in the case of a ferromagnetic to anti-ferromagnetic transition, such persistent phase coexistence has now been reported across a variety of first-order magnetic transitions. These include colossal-magnetoresistance manganite materials, magnetocaloric materials, magnetic shape memory materials, and other materials. The interesting feature of these observations of
2280:
properties of phase transitions: the change of macroscopic behavior and the coherence of a system at a critical point. Phase transitions are prominent feature of motor behavior in biological systems. Spontaneous gait transitions, as well as fatigue-induced motor task disengagements, show typical critical behavior as an intimation of the sudden qualitative change of the previously stable motor behavioral pattern.
5070:
576:
1621:
possibilities. On cooling, some liquids vitrify into a glass rather than transform to the equilibrium crystal phase. This happens if the cooling rate is faster than a critical cooling rate, and is attributed to the molecular motions becoming so slow that the molecules cannot rearrange into the crystal positions. This slowing down happens below a glass-formation temperature
2249:, gel to liquid crystalline phase transitions play a critical role in physiological functioning of biomembranes. In gel phase, due to low fluidity of membrane lipid fatty-acyl chains, membrane proteins have restricted movement and thus are restrained in exercise of their physiological role. Plants depend critically on photosynthesis by
1471:. During such a transition, a system either absorbs or releases a fixed (and typically large) amount of energy per volume. During this process, the temperature of the system will stay constant as heat is added: the system is in a "mixed-phase regime" in which some parts of the system have completed the transition and others have not.
1452:
approximations, which had predicted that it has a simple discontinuity at critical temperature. Instead, the exact specific heat had a logarithmic divergence at the critical temperature. In the following decades, the
Ehrenfest classification was replaced by a simplified classification scheme that is
1400:
exhibit a discontinuity in the first derivative of the free energy with respect to some thermodynamic variable. The various solid/liquid/gas transitions are classified as first-order transitions because they involve a discontinuous change in density, which is the (inverse of the) first derivative of
2279:
in the salamander retina, bird flocks gene expression networks in
Drosophila, and protein folding. However, it is not clear whether or not alternative reasons could explain some of the phenomena supporting arguments for criticality. It has also been suggested that biological organisms share two key
1635:
falls within this range, then there is an interesting possibility that the transition is arrested when it is partial and incomplete. Extending these ideas to first-order magnetic transitions being arrested at low temperatures, resulted in the observation of incomplete magnetic transitions, with two
1606:
state, and its entropy, density, and so on, depend on the thermal history. Therefore, the glass transition is primarily a dynamic phenomenon: on cooling a liquid, internal degrees of freedom successively fall out of equilibrium. Some theoretical methods predict an underlying phase transition in the
1643:
falling within the temperature range over which the transition occurs is that the first-order magnetic transition is influenced by magnetic field, just like the structural transition is influenced by pressure. The relative ease with which magnetic fields can be controlled, in contrast to pressure,
1620:
A disorder-broadened first-order transition occurs over a finite range of temperatures where the fraction of the low-temperature equilibrium phase grows from zero to one (100%) as the temperature is lowered. This continuous variation of the coexisting fractions with temperature raised interesting
2295:
to hydrophobic, causing the former to lie near the globular surface, while the latter lie closer to the globular center. Twenty fractals were discovered in solvent associated surface areas of > 5000 protein segments. The existence of these fractals proves that proteins function near critical
2177:
theory of phase transitions, which states that the thermodynamic properties of a system near a phase transition depend only on a small number of features, such as dimensionality and symmetry, and are insensitive to the underlying microscopic properties of the system. Again, the divergence of the
1694:: each point in the fluid has the same properties, but each point in a crystal does not have the same properties (unless the points are chosen from the lattice points of the crystal lattice). Typically, the high-temperature phase contains more symmetries than the low-temperature phase due to
1424:
In practice, only the first- and second-order phase transitions are typically observed. The second-order phase transition was for a while controversial, as it seems to require two sheets of the Gibbs free energy to osculate exactly, which is so unlikely as to never occur in practice.
1670:, at which the transition between liquid and gas becomes a second-order transition. Near the critical point, the fluid is sufficiently hot and compressed that the distinction between the liquid and gaseous phases is almost non-existent. This is associated with the phenomenon of
1409:, which is the first derivative of the free energy with respect to the external field, is continuous across the transition) but exhibit discontinuity in a second derivative of the free energy. These include the ferromagnetic phase transition in materials such as iron, where the
2299:
In groups of organisms in stress (when approaching critical transitions), correlations tend to increase, while at the same time, fluctuations also increase. This effect is supported by many experiments and observations of groups of people, mice, trees, and grassy plants.
303:. Such a diagram usually depicts states in equilibrium. A phase transition usually occurs when the pressure or temperature changes and the system crosses from one region to another, like water turning from liquid to solid as soon as the temperature drops below the
1972:
The critical exponents are not necessarily the same above and below the critical temperature. When a continuous symmetry is explicitly broken down to a discrete symmetry by irrelevant (in the renormalization group sense) anisotropies, then some exponents (such as
680:). This condition generally stems from the interactions of a large number of particles in a system, and does not appear in systems that are small. Phase transitions can occur for non-thermodynamic systems, where temperature is not a parameter. Examples include:
2172:
More impressively, but understandably from above, they are an exact match for the critical exponents of the ferromagnetic phase transition in uniaxial magnets. Such systems are said to be in the same universality class. Universality is a prediction of the
1757:
and ferromagnetic, can have order parameters for more than one degree of freedom. In such phases, the order parameter may take the form of a complex number, a vector, or even a tensor, the magnitude of which goes to zero at the phase transition.
404:
to equilibrium phase transformation for structural phase transitions. A metastable polymorph which forms rapidly due to lower surface energy will transform to an equilibrium phase given sufficient thermal input to overcome an energetic barrier.
2012:= −0.013 ± 0.003. At least one experiment was performed in the zero-gravity conditions of an orbiting satellite to minimize pressure differences in the sample. This experimental value of α agrees with theoretical predictions based on
1718:
is a measure of the degree of order across the boundaries in a phase transition system; it normally ranges between zero in one phase (usually above the critical point) and nonzero in the other. At the critical point, the order parameter
1599:
far below the melting point of the crystalline phase. This is atypical in several respects. It is not a transition between thermodynamic ground states: it is widely believed that the true ground state is always crystalline. Glass is a
684:, dynamic phase transitions, and topological (structural) phase transitions. In these types of systems other parameters take the place of temperature. For instance, connection probability replaces temperature for percolating networks.
3013:
Kumar, Kranti; Pramanik, A. K.; Banerjee, A.; Chaddah, P.; Roy, S. B.; Park, S.; Zhang, C. L.; Cheong, S.-W. (2006). "Relating supercooling and glass-like arrest of kinetics for phase separated systems: DopedCeFe2and(La,Pr,Ca)MnO3".
5039:, 1991. Very well-written book in "semi-popular" style—not a textbook—aimed at an audience with some training in mathematics and the physical sciences. Explains what scaling in phase transitions is all about, among other things.
1432:
The
Ehrenfest classification implicitly allows for continuous phase transformations, where the bonding character of a material changes, but there is no discontinuity in any free energy derivative. An example of this occurs at the
1490:
can broaden a first-order transition. That is, the transformation is completed over a finite range of temperatures, but phenomena like supercooling and superheating survive and hysteresis is observed on thermal cycling.
147:, have identical free energies and therefore are equally likely to exist. Below the boiling point, the liquid is the more stable state of the two, whereas above the boiling point the gaseous form is the more stable.
2149:
2038:
Some model systems do not obey a power-law behavior. For example, mean field theory predicts a finite discontinuity of the heat capacity at the transition temperature, and the two-dimensional Ising model has a
2256:
which are exposed cold environmental temperatures. Thylakoid membranes retain innate fluidity even at relatively low temperatures because of high degree of fatty-acyl disorder allowed by their high content of
1833:, and they have been discovered to have many interesting properties. The phenomena associated with continuous phase transitions are called critical phenomena, due to their association with critical points.
1737:
From a theoretical perspective, order parameters arise from symmetry breaking. When this happens, one needs to introduce one or more extra variables to describe the state of the system. For example, in the
1534:
transition. In contrast to viscosity, thermal expansion and heat capacity of amorphous materials show a relatively sudden change at the glass transition temperature which enables accurate detection using
3537:
Roy, S. B.; Chattopadhyay, M. K.; Chaddah, P.; Moore, J. D.; Perkins, G. K.; Cohen, L. F.; Gschneidner, K. A.; Pecharsky, V. K. (2006). "Evidence of a magnetic glass state in the magnetocaloric material
4757:
2214:
classes. In addition to the critical exponents, there are also universal relations for certain static or dynamic functions of the magnetic fields and temperature differences from the critical value.
1941:
2350:(simultaneous measurement of magnetic and non-magnetic transitions. No temperature limits. Over 2000 °C already performed, theoretical possible up to the highest crystal material, such as
2261:, 18-carbon chain with 3-double bonds. Gel-to-liquid crystalline phase transition temperature of biological membranes can be determined by many techniques including calorimetry, fluorescence,
1429:
replied the criticism by pointing out that the Gibbs free energy surface might have two sheets on one side, but only one sheet on the other side, creating a forked appearance. ( pp. 146--150)
1781:. As the universe expanded and cooled, the vacuum underwent a series of symmetry-breaking phase transitions. For example, the electroweak transition broke the SU(2)×U(1) symmetry of the
533:
transformation, in which a two-component single-phase liquid is cooled and transforms into two solid phases. The same process, but beginning with a solid instead of a liquid is called a
2272:
by recording measurements of the concerned parameter by at series of sample temperatures. A simple method for its determination from 13-C NMR line intensities has also been proposed.
1396:
as a function of other thermodynamic variables. Under this scheme, phase transitions were labeled by the lowest derivative of the free energy that is discontinuous at the transition.
2291:
properties. It has long been known that protein globules are shaped by interactions with water. There are 20 amino acids that form side groups on protein peptide chains range from
4083:
D.Y. Lando and V.B. Teif (2000). "Long-range interactions between ligands bound to a DNA molecule give rise to adsorption with the character of phase transition of the first kind".
4204:
Tkacik, Gasper; Mora, Thierry; Marre, Olivier; Amodei, Dario; Berry II, Michael J.; Bialek, William (2014). "Thermodynamics for a network of neurons: Signatures of criticality".
1413:, which is the first derivative of the free energy with respect to the applied magnetic field strength, increases continuously from zero as the temperature is lowered below the
3360:
Manekar, M. A.; Chaudhary, S.; Chattopadhyay, M. K.; Singh, K. J.; Roy, S. B.; Chaddah, P. (2001). "First-order transition from antiferromagnetism to ferromagnetism inCe(Fe
3674:
Kushwaha, Pallavi; Lakhani, Archana; Rawat, R.; Chaddah, P. (2009). "Low-temperature study of field-induced antiferromagnetic-ferromagnetic transition in Pd-doped Fe-Rh".
2315:
2309:
4600:
Hristovski, R.; Balagué, N. (2010). "Fatigue-induced spontaneous termination point--nonequilibrium phase transitions and critical behavior in quasi-isometric exertion".
2318:
is that when a conflict that is non-violent shifts to a phase of armed conflict, this is a phase transition from latent to manifest phases within the dynamical system.
3075:
Pasquini, G.; Daroca, D. Pérez; Chiliotte, C.; Lozano, G. S.; Bekeris, V. (2008). "Ordered, Disordered, and
Coexistent Stable Vortex Lattices inNbSe2Single Crystals".
1991:
3433:
Banerjee, A.; Pramanik, A. K.; Kumar, Kranti; Chaddah, P. (2006). "Coexisting tunable fractions of glassy and equilibrium long-range-order phases in manganites".
3486:
Wu W.; Israel C.; Hur N.; Park S.; Cheong S. W.; de
Lozanne A. (2006). "Magnetic imaging of a supercooling glass transition in a weakly disordered ferromagnet".
2066:, are defined, examining the power law behavior of a measurable physical quantity near the phase transition. Exponents are related by scaling relations, such as
2314:
Phase transitions have been hypothesised to occur in social systems viewed as dynamical systems. A hypothesis proposed in the 1990s and 2000s in the context of
1658:
in an exhaustive way. Phase coexistence across first-order magnetic transitions will then enable the resolution of outstanding issues in understanding glasses.
4875:
4736:
100:, resulting in an abrupt change in volume. The identification of the external conditions at which a transformation occurs defines the phase transition point.
179:
2165:
It is a remarkable fact that phase transitions arising in different systems often possess the same set of critical exponents. This phenomenon is known as
4745:
1366:
1761:
There also exist dual descriptions of phase transitions in terms of disorder parameters. These indicate the presence of line-like excitations such as
1796:
Progressive phase transitions in an expanding universe are implicated in the development of order in the universe, as is illustrated by the work of
3769:
2169:. For example, the critical exponents at the liquid–gas critical point have been found to be independent of the chemical composition of the fluid.
365:
Phase transitions can also occur when a solid changes to a different structure without changing its chemical makeup. In elements, this is known as
88:. During a phase transition of a given medium, certain properties of the medium change as a result of the change of external conditions, such as
5087:
3977:
Lipa, J.; Nissen, J.; Stricker, D.; Swanson, D.; Chui, T. (2003). "Specific heat of liquid helium in zero gravity very near the lambda point".
1789:. This transition is important to explain the asymmetry between the amount of matter and antimatter in the present-day universe, according to
2072:
664:), the heavier water isotopes (O and H) become enriched in the liquid phase while the lighter isotopes (O and H) tend toward the vapor phase.
17:
1507:
546:
121:, showing whether solid ice, liquid water, or gaseous water vapor is the most stable at different combinations of temperature and pressure.
1946:
The heat capacity of amorphous materials has such a behaviour near the glass transition temperature where the universal critical exponent
1852:
of the system while keeping all the other thermodynamic variables fixed and find that the transition occurs at some critical temperature
5025:
Mussardo G., "Statistical Field Theory. An
Introduction to Exactly Solved Models of Statistical Physics", Oxford University Press, 2010.
1461:
In the modern classification scheme, phase transitions are divided into two broad categories, named similarly to the
Ehrenfest classes:
5115:
2393:
2043:
divergence. However, these systems are limiting cases and an exception to the rule. Real phase transitions exhibit power-law behavior.
583:
shows two concurrent phase changes. The transition from solid to liquid, and gas to liquid (shown by the white condensed water vapour).
1607:
hypothetical limit of infinitely long relaxation times. No direct experimental evidence supports the existence of these transitions.
2027:< 1, the enthalpy stays finite). An example of such behavior is the 3D ferromagnetic phase transition. In the three-dimensional
315:) in such a way that it can be brought past a phase transition point without undergoing a phase transition. The resulting state is
172:
1530:
the phase transition is second-order for both normal-state–mixed-state and mixed-state–superconducting-state transitions) and the
2948:
1666:
In any system containing liquid and gaseous phases, there exists a special combination of pressure and temperature, known as the
1434:
150:
Common transitions between the solid, liquid, and gaseous phases of a single component, due to the effects of temperature and/or
510:
are more complicated than transitions involving a single compound. While chemically pure compounds exhibit a single temperature
1674:, a milky appearance of the liquid due to density fluctuations at all possible wavelengths (including those of visible light).
1359:
549:
reaction consists of change from a liquid and to a combination of a solid and a second liquid, where the two liquids display a
541:
transformation, in which a two-component single-phase solid is heated and transforms into a solid phase and a liquid phase. A
4859:
4549:
3837:
3746:
2840:
2721:
2545:
4926:
1628:, which may depend on the applied pressure. If the first-order freezing transition occurs over a range of temperatures, and
1884:
1734:
system undergoing a phase transition. For liquid/gas transitions, the order parameter is the difference of the densities.
1440:
The first example of a phase transition which did not fit into the
Ehrenfest classification was the exact solution of the
3589:
Lakhani, Archana; Banerjee, A.; Chaddah, P.; Chen, X.; Ramanujan, R. V. (2012). "Magnetic glass in shape memory alloy: Ni
2628:
2206:
before the phase transition, as a consequence of lower degree of stability of the initial phase of the system. The large
165:
319:, i.e., less stable than the phase to which the transition would have occurred, but not unstable either. This occurs in
1569:
60:
of transition between one state of a medium and another. Commonly the term is used to refer to changes among the basic
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4911:
4903:
2419:
1536:
1352:
1339:
2515:
2000:< 0, the heat capacity has a "kink" at the transition temperature. This is the behavior of liquid helium at the
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393:
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336:
1321:
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2013:
1720:
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1515:
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5377:
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1104:
656:
occurs during a phase transition, the ratio of light to heavy isotopes in the involved molecules changes. When
460:
232:
5564:
5392:
5018:
2674:
Jaeger, Gregg (1 May 1998). "The
Ehrenfest Classification of Phase Transitions: Introduction and Evolution".
2509:
2457:
2425:
2347:
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263:
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4030:
Kleinert, Hagen (1999). "Critical exponents from seven-loop strong-coupling φ4 theory in three dimensions".
5574:
5447:
5192:
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Leonard, F.; Delamotte, B. (2015). "Critical exponents can be different on the two sides of a transition".
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1279:
759:
632:
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5625:
4995:
4635:
Moret, Marcelo; Zebende, Gilney (January 2007). "Amino acid hydrophobicity and accessible surface area".
3191:
Lubchenko, V. Wolynes; Wolynes, Peter G. (2007). "Theory of
Structural Glasses and Supercooled Liquids".
2339:(simultaneous measurement of magnetic and non-magnetic transitions. Limited up to about 800–1000 °C)
2227:
1474:
Familiar examples are the melting of ice or the boiling of water (the water does not instantly turn into
522:
resulting in a temperature span where solid and liquid coexist in equilibrium. This is often the case in
299:
For a single component, the most stable phase at different temperatures and pressures can be shown on a
5620:
4915:
1284:
909:
478:
389:
2764:
5101:
3867:
2737:
Gross, David J. (1980), "Possible third-order phase transition in the large N lattice gauge theory",
2645:
1808:
1393:
1174:
849:
669:
661:
4565:
Diedrich, F. J.; Warren, W. H. Jr. (1995). "Why change gaits? Dynamics of the walk-run transition".
2336:
1829:
Continuous phase transitions are easier to study than first-order transitions due to the absence of
5599:
5498:
5128:
2478:
2351:
2276:
2275:
It has been proposed that some biological systems might lie near critical points. Examples include
1790:
1577:
1169:
1164:
690:
681:
2978:
Imry, Y.; Wortis, M. (1979). "Influence of quenched impurities on first-order phase transitions".
1254:
5493:
1750:. However, note that order parameters can also be defined for non-symmetry-breaking transitions.
1426:
1418:
859:
1264:
5518:
5508:
5258:
5253:
4992:
Constitutions of matter : mathematically modelling the most everyday of physical phenomena
4776:
1527:
1249:
1189:
1159:
1109:
829:
719:
557:
428:
96:. This can be a discontinuous change; for example, a liquid may become gas upon heating to its
3736:
3222:
5005:
2408:
2242:, and cooperative ligand binding to DNA and proteins with the character of phase transition.
2174:
1976:
1786:
1523:
1289:
904:
889:
653:
5437:
5197:
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4821:
4738:
Complexity Theory and Conflict Transformation: An Exploration of Potential and Implications
4701:
4644:
4439:
4382:
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4248:
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3996:
3935:
3882:
3693:
3624:
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3316:
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3210:
3156:
3094:
3033:
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2798:
2786:
2584:
1691:
1671:
879:
769:
519:
514:
between solid and liquid phases, mixtures can either have a single melting point, known as
503:
307:. In exception to the usual case, it is sometimes possible to change the state of a system
289:
81:
2326:
A variety of methods are applied for studying the various effects. Selected examples are:
1840:. The most important one is perhaps the exponent describing the divergence of the thermal
650:
in the laws of physics during the early history of the universe as its temperature cooled.
392:
occurs as one of the many phase transformations in carbon steel and stands as a model for
8:
5412:
5304:
5294:
5207:
5162:
3636:
2434:
2342:
1699:
1554:
1119:
929:
779:
312:
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4825:
4705:
4648:
4542:
Dynamic Patterns: The Self-Organization of Brain and Behavior (Complex Adaptive Systems)
4443:
4386:
4363:
Mora, Thierry; Bialek, William (2011). "Are biological systems poised at criticality?".
4321:
4252:
4167:"Determination of membrane lipid phase transition temperature from 13-C NMR intensities"
4053:
4000:
3939:
3886:
3697:
3628:
3559:
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3456:
3395:
3320:
3265:
3214:
3160:
3098:
3037:
2991:
2790:
2588:
2222:
Phase transitions play many important roles in biological systems. Examples include the
467:. A simplified but highly useful model of magnetic phase transitions is provided by the
135:
Phase transitions commonly refer to when a substance transforms between one of the four
5559:
5488:
5322:
4784:
4717:
4691:
4522:
4496:
4460:
4429:
4417:
4398:
4372:
4340:
4307:
4295:
4271:
4238:
4227:"Social interactions dominate speed control in poising natural flocks near criticality"
4226:
4205:
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4012:
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3925:
3898:
3806:
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3717:
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Ojovan, M.I. (2013). "Ordering and structural changes at the glass-liquid transition".
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Apart from isolated, simple phase transitions, there exist transition lines as well as
1299:
1259:
1234:
982:
973:
424:
414:
397:
354:
346:
3894:
3464:
2765:"Top eigenvalue of a random matrix: large deviations and third order phase transition"
5589:
5584:
5554:
5513:
5402:
5354:
5339:
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5202:
5042:
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3709:
3660:
3648:
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3571:
3511:
3407:
3334:
3289:
3277:
3226:
3181:
Gotze, Wolfgang. "Complex Dynamics of Glass-Forming Liquids: A Mode-Coupling Theory."
3168:
3118:
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3049:
2930:
2912:
2873:
2836:
2814:
2802:
2717:
2695:
2649:
2610:
2563:"Phase diagram for the transition from photonic crystals to dielectric metamaterials"
2541:
2448:
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2001:
1837:
1824:
1782:
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1703:
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1683:
1602:
1487:
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1414:
1229:
1074:
964:
884:
673:
647:
614:
515:
436:
374:
350:
85:
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4016:
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3902:
3810:
3783:
Clark, J.B.; Hastie, J.W.; Kihlborg, L.H.E.; Metselaar, R.; Thackeray, M.M. (1994).
3472:
3419:
3238:
2629:
Semiconductors and Semimetals. Vol 100. Photonic Crystal Metasurface Optoelectronics
113:
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4609:
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4390:
4335:
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4266:
4256:
4178:
4139:
4096:
4092:
4057:
4004:
3947:
3943:
3890:
3796:
3701:
3632:
3563:
3523:
3503:
3460:
3399:
3346:
3324:
3269:
3218:
3164:
3130:
3106:
3102:
3041:
2995:
2904:
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2794:
2746:
2683:
2600:
2592:
2368:
2239:
1588:
934:
899:
894:
854:
794:
754:
560:, in which a single phase is cooled and separates into two different compositions.
215:
77:
57:
4721:
4526:
4402:
3273:
2390: – Property of some chemical elements to exist in two or more different forms
2283:
The characteristic feature of second order phase transitions is the appearance of
5534:
5387:
5124:
4942:
4802:
4798:
2963:
2503:
2231:
1244:
1194:
1064:
819:
731:
564:
550:
378:
136:
61:
4713:
4613:
2493: – Mathematical theory on behavior of connected clusters in a random graph
2466: – Theory of continuous phase transitions of second order phase transitions
2023:< 1, the heat capacity diverges at the transition temperature (though, since
1844:
by approaching the transition. For instance, let us examine the behavior of the
5332:
5327:
5284:
5217:
5212:
4922:
4883:
4656:
4578:
4061:
4008:
3705:
3567:
3403:
3045:
2893:"The Ehrenfest Classification of Phase Transitions: Introduction and Evolution"
2402:
2258:
1969:. Its actual value depends on the type of phase transition we are considering.
1762:
1519:
1389:
1326:
1294:
1274:
1269:
1224:
1144:
1079:
977:
864:
709:
677:
596:
523:
440:
341:
304:
126:
4948:
4833:
4394:
2536:
Askeland, Donald R.; Haddleton, Frank; Green, Phil; Robertson, Howard (1996).
419:
5614:
5569:
5549:
5472:
5432:
5367:
5299:
5222:
5052:
5036:
4891:
3713:
3644:
3575:
3411:
3114:
3053:
2999:
2916:
2877:
2806:
2463:
2223:
2031:
for uniaxial magnets, detailed theoretical studies have yielded the exponent
1845:
1797:
1743:
1739:
1731:
1727:
1547:
1410:
1005:
986:
968:
869:
789:
636:
511:
444:
382:
300:
140:
130:
97:
4753:
4330:
4261:
3801:
3784:
2750:
2310:
Complex system approach to peace and armed conflict § Phase transitions
1746:, whose direction was spontaneously chosen when the system cooled below the
1199:
139:
to another. At the phase transition point for a substance, for instance the
5594:
5467:
5462:
5457:
5422:
5372:
5289:
4999:
4664:
4621:
4518:
4469:
4349:
4280:
4104:
3955:
3652:
3515:
3338:
3281:
3230:
3122:
2614:
1801:
1596:
1557:, when varying external parameters like the magnetic field or composition.
1445:
1219:
1209:
1179:
1139:
1134:
1114:
959:
939:
799:
621:
491:
324:
320:
268:
251:
5093:
4586:
4190:
4151:
2908:
2687:
435:
Phase transitions can also describe the change between different kinds of
5503:
5397:
5309:
4794:
4790:
4485:"From physics to biology by extending criticality and symmetry breakings"
3991:
3447:
3386:
3205:
3028:
2439:
2330:
2292:
2250:
2235:
2028:
1836:
Continuous phase transitions can be characterized by parameters known as
1830:
1747:
1483:
1475:
1468:
1441:
1304:
1239:
1214:
1184:
1129:
1124:
1056:
698:
657:
545:
reaction is a peritectoid rection, except involving only solid phases. A
542:
495:
468:
456:
452:
89:
4847:
4812:(1974). "The renormalization group in the theory of critical behavior".
2892:
2869:
2596:
2144:{\displaystyle \beta =\gamma /(\delta -1),\quad \nu =\gamma /(2-\eta ).}
617:
in certain metals and ceramics when cooled below a critical temperature.
327:, for example. Metastable states do not appear on usual phase diagrams.
36:
This diagram shows the nomenclature for the different phase transitions.
5442:
5417:
5344:
5314:
5248:
5227:
4044:
3785:"Definitions of terms relating to phase transitions of the solid state"
2262:
2005:
1540:
1531:
1479:
1149:
991:
784:
624:
properties in artificial photonic media as their parameters are varied.
603:
538:
529:
There are also a number of phase transitions involving three phases: a
464:
401:
316:
275:
2833:
Elements of classical thermodynamics: for advanced students of physics
1526:
the phase transition is second-order at zero external field and for a
4418:"Zipf's law and criticality in multivariate data without fine-tuning"
3507:
2442: – Mathematical model of ferromagnetism in statistical mechanics
2387:
2040:
1875:
1511:
1204:
1154:
1027:
874:
774:
592:
534:
482:
A binary phase diagram showing the most stable chemical compounds of
366:
358:
308:
45:
5177:
5033:
Fractals, chaos, power laws : minutes from an infinite paradise
4567:
Journal of Experimental Psychology. Human Perception and Performance
4484:
3329:
3304:
2154:
It can be shown that there are only two independent exponents, e.g.
1506:. They are characterized by a divergent susceptibility, an infinite
32:
5579:
5407:
4128:"C NMR studies of lipid fatty acyl chains of chloroplast membranes"
3930:
2856:
Austin, J. B. (November 1932). "Heat Capacity of Iron - A Review".
2579:
1592:
1573:
764:
607:
530:
483:
244:
151:
93:
4877:
Ice Phase Transition as a sample of finite system phase transition
4696:
4501:
4434:
4377:
4312:
4243:
4210:
3688:
3619:
3359:
3089:
2781:
5539:
5427:
5362:
5279:
5274:
2284:
2202:. Connected to the previous phenomenon is also the phenomenon of
1084:
1069:
1032:
1023:
1018:
507:
455:. Another example is the transition between differently ordered,
227:
41:
1644:
raises the possibility that one can study the interplay between
5148:
5069:
4959:(1974). "The Renormalization Group and the epsilon-Expansion".
4895:
4879:, (Physics Education (India) Volume 32. No. 2, Apr - Jun 2016)
4728:
2535:
1037:
1013:
744:
640:
487:
448:
205:
69:
1818:
1777:
Symmetry-breaking phase transitions play an important role in
575:
5157:
5143:
3074:
2711:
2518: – Field theory involving topological effects in physics
2362:
1042:
739:
628:
580:
200:
144:
118:
65:
27:
Physical process of transition between basic states of matter
4921:
4851:
Chaos, Phase Transitions, Topology Change and Path Integrals
3782:
3536:
3432:
3012:
2396: – Chemical reaction whose product is also its catalyst
4842:
Lectures on Phase Transitions and the Renormalization Group
4680:"Correlations, risk and crisis: From physiology to finance"
4678:
Gorban, A.N.; Smirnova, E.V.; Tyukina, T.A. (August 2010).
3673:
3485:
3868:"Topologically disordered systems at the glass transition"
3588:
2217:
2194:. As a consequence, at a phase transition one may observe
1392:
classified phase transitions based on the behavior of the
5153:
3976:
2269:
1993:, the exponent of the susceptibility) are not identical.
749:
210:
73:
5047:
Introduction to Phase Transitions and Critical Phenomena
4293:
4082:
2935:
Introduction to Phase Transitions and Critical Phenomena
2835:(Repr ed.). Cambridge: Univ. Pr. pp. 140–141.
2428: – Shift of atomic positions in a crystal structure
385:) are all examples of solid to solid phase transitions.
4416:
Schwab, David J; Nemenman, Ilya; Mehta, Pankaj (2014).
3735:
Ivancevic, Vladimir G.; Ivancevic, Tijiana, T. (2008).
2769:
Journal of Statistical Mechanics: Theory and Experiment
2444:
Pages displaying short descriptions of redirect targets
2430:
Pages displaying short descriptions of redirect targets
2398:
Pages displaying short descriptions of redirect targets
2186:
There are also other critical phenomena; e.g., besides
4998:, 1996. Contains a detailed pedagogical discussion of
3854:
Cosmogenesis, The Development of Order in the Universe
2763:
Majumdar, Satya N; Schehr, Grégory (31 January 2014).
2303:
4684:
Physica A: Statistical Mechanics and Its Applications
4677:
4294:
Krotov, D; Dubuis, J O; Gregor, T; Bialek, W (2014).
4224:
4203:
2460: – Noncontact variant of atomic force microscopy
2075:
1979:
1936:{\displaystyle C\propto |T_{\text{c}}-T|^{-\alpha }.}
1887:
1686:
process. For instance, the cooling of a fluid into a
1518:. Examples of second-order phase transitions are the
5049:(Oxford University Press, Oxford and New York 1971).
3530:
3353:
3142:
3140:
2712:
Blundell, Stephen J.; Katherine M. Blundell (2008).
2474:
Pages displaying wikidata descriptions as a fallback
2453:
Pages displaying wikidata descriptions as a fallback
2413:
Pages displaying wikidata descriptions as a fallback
2238:, liquid crystal-like transitions in the process of
2210:
of a continuous phase transition split into smaller
1448:. The exact specific heat differed from the earlier
439:. The most well-known is the transition between the
4848:Ivancevic, Vladimir G; Ivancevic, Tijana T (2008),
4746:
Department of Peace Studies, University of Bradford
4415:
3667:
3582:
4539:
3825:
3734:
3068:
2506: – Thin layer of liquid in a superfluid state
2143:
1985:
1935:
606:geometry on coverage and temperature, such as for
4799:Fundamentals of Multiphase Heat Transfer and Flow
4599:
3137:
3006:
2965:Fundamentals of Multiphase Heat Transfer and Flow
2405: – Major stage of a crystallization process
1950:= 0.59 A similar behavior, but with the exponent
5612:
3915:
3190:
1848:near such a transition. We vary the temperature
676:for some choice of thermodynamic variables (cf.
563:Non-equilibrium mixtures can occur, such as in
4734:
4564:
4171:Journal of Biochemical and Biophysical Methods
2762:
2481: – Different known phase of states matter
1522:transition, superconducting transition (for a
595:between solid and liquid, such as one of the "
556:Separation into multiple phases can occur via
526:, where the two components are isostructural.
451:materials, which occurs at what is called the
396:. Order-disorder transitions such as in alpha-
381:, or from one amorphous structure to another (
5109:
4482:
4132:Indian Journal of Biochemistry and Biophysics
2650:"Fundamentals of Stable Isotope Geochemistry"
2644:
1360:
400:. As with states of matter, there are also a
173:
4634:
4489:Progress in Biophysics and Molecular Biology
4119:
3866:Ojovan, Michael I.; Lee, William E. (2006).
3768:: CS1 maint: multiple names: authors list (
2669:
2667:
1726:An example of an order parameter is the net
1610:
1482:mixture of liquid water and vapor bubbles).
1405:are continuous in the first derivative (the
103:
5123:
4954:
4225:Bialek, W; Cavagna, A; Giardina, I (2014).
2560:
2296:points of second-order phase transitions.
2178:correlation length is the essential point.
1819:Critical exponents and universality classes
1384:
377:to another, from a crystalline solid to an
349:, distinguishing between several different
48:, and other related fields like biology, a
5116:
5102:
5057:Statistical Mechanics of Phase Transitions
4362:
3305:"Materials science: Metal turned to glass"
2977:
2707:
2705:
2394:Autocatalytic reactions and order creation
1785:into the U(1) symmetry of the present-day
1706:, which only occurs at low temperatures).
1401:the free energy with respect to pressure.
1367:
1353:
697:
180:
166:
5082:Interactive Phase Transitions on lattices
4781:Basic Notions of Condensed Matter Physics
4695:
4500:
4483:Longo, G.; Montévil, M. (1 August 2011).
4459:
4433:
4376:
4339:
4329:
4311:
4270:
4260:
4242:
4209:
4043:
3990:
3929:
3865:
3800:
3687:
3618:
3446:
3385:
3328:
3252:Greer, A. L. (1995). "Metallic Glasses".
3223:10.1146/annurev.physchem.58.032806.104653
3204:
3088:
3027:
2950:Transport Phenomena in Multiphase Systems
2780:
2664:
2604:
2578:
2451: – apparent change of physical state
1772:
1456:
463:, magnetic structures, such as in cerium
4029:
3823:
2538:The Science and Engineering of Materials
2008:state, for which experiments have found
574:
477:
418:
340:
112:
31:
4164:
4125:
2929:
2830:
2702:
2218:Phase transitions in biological systems
579:A small piece of rapidly melting solid
154:are identified in the following table:
143:, the two phases involved - liquid and
14:
5613:
4808:
3741:. Berlin: Springer. pp. 176–177.
3302:
3146:
2890:
2858:Industrial & Engineering Chemistry
2855:
2673:
1958:, applies for the correlation length.
1453:able to incorporate such transitions.
369:, whereas in compounds it is known as
84:and the states of matter have uniform
5097:
4763:from the original on 26 November 2022
3251:
2897:Archive for History of Exact Sciences
2736:
2676:Archive for History of Exact Sciences
2365:(measurement of magnetic transitions)
2333:(measurement of magnetic transitions)
2181:
1406:
3875:Journal of Physics: Condensed Matter
3607:Journal of Physics: Condensed Matter
3435:Journal of Physics: Condensed Matter
2826:
2824:
2411: – materials science phenomenon
1965:is positive. This is different with
1615:
5002:'s solution of the 2-D Ising Model.
4916:physik.fu-berlin.de readable online
3193:Annual Review of Physical Chemistry
2540:. Chapman & Hall. p. 286.
2304:Phase transitions in social systems
1709:
1564:. They are continuous but break no
1550:of second-order phase transitions.
1435:supercritical liquid–gas boundaries
108:
24:
4904:World Scientific (Singapore, 1989)
4770:
2422: – Thermoanalytical technique
2046:Several other critical exponents,
1682:Phase transitions often involve a
1661:
1379:
423:A phase diagram showing different
25:
5642:
5063:
5022:, Pergamon Press, 3rd Ed. (1994).
4928:Critical Properties of φ-Theories
2953:, Elsevier, Burlington, MA, 2006,
2821:
2561:Rybin, M.V.; et al. (2015).
2512: – Process in quantum optics
2420:Differential scanning calorimetry
1568:. The most famous example is the
1560:Several transitions are known as
1537:differential scanning calorimetry
668:Phase transitions occur when the
570:
520:liquidus and solidus temperatures
427:in the same crystal structure of
5176:
5068:
5059:, Oxford University Press, 1992.
4888:Gauge Fields in Condensed Matter
4511:10.1016/j.pbiomolbio.2011.03.005
3169:10.1016/j.jnoncrysol.2013.10.016
2799:10.1088/1742-5468/2014/01/P01012
2516:Topological quantum field theory
2487: – Crystal growth technique
2472: – crystal growth technique
1753:Some phase transitions, such as
1742:phase, one must provide the net
1698:, with the exception of certain
1562:infinite-order phase transitions
1334:
1333:
1320:
394:displacive phase transformations
337:Polymorphism (materials science)
286:
284:
255:
236:
4671:
4628:
4593:
4558:
4533:
4476:
4409:
4356:
4287:
4218:
4197:
4158:
4076:
4023:
3970:
3909:
3859:
3846:
3817:
3776:
3728:
3479:
3426:
3296:
3245:
3184:
3175:
2971:
2956:
2941:
2923:
2884:
2849:
2321:
2266:electron paramagnetic resonance
2108:
2014:variational perturbation theory
1486:and Michael Wortis showed that
117:A simplified phase diagram for
4491:. Systems Biology and Cancer.
4452:10.1103/PhysRevLett.113.068102
4365:Journal of Statistical Physics
4296:"Morphogenesis at criticality"
4097:10.1080/07391102.2000.10506578
3948:10.1103/PhysRevLett.115.200601
3637:10.1088/0953-8984/24/38/386004
3107:10.1103/PhysRevLett.100.247003
2968:, Springer, New York, NY, 2020
2756:
2730:
2638:
2621:
2554:
2529:
2135:
2123:
2102:
2090:
1917:
1895:
1595:and other liquids that can be
1582:two-dimensional electron gases
1570:Kosterlitz–Thouless transition
1504:"continuous phase transitions"
1403:Second-order phase transitions
13:
1:
5565:Macroscopic quantum phenomena
5019:Course of Theoretical Physics
3274:10.1126/science.267.5206.1947
2523:
2510:Superradiant phase transition
2458:Kelvin probe force microscope
2426:Diffusionless transformations
2348:Perturbed angular correlation
1702:(e.g. the formation of heavy
1696:spontaneous symmetry breaking
1565:
1497:Second-order phase transition
1465:First-order phase transitions
1398:First-order phase transitions
587:Other phase changes include:
330:
18:Second order phase transition
5575:Order and disorder (physics)
4981:10.1016/0370-1573(74)90023-4
4925:; Verena Schulte-Frohlinde.
4874:M.R. Khoshbin-e-Khoshnazar,
4844:, Perseus Publishing (1992).
4735:Diane Hendrick (June 2009),
4183:10.1016/0165-022X(90)90097-V
4144:10.1016/0165-022X(91)90019-S
3832:. Harvard University Press.
2891:Jaeger, Gregg (1 May 1998).
2627:Eds. Zhou, W., and Fan. S.,
2497:Continuum percolation theory
2470:Laser-heated pedestal growth
502:Phase transitions involving
345:A phase diagram showing the
7:
4996:University of Chicago Press
4714:10.1016/j.physa.2010.03.035
4614:10.1016/j.humov.2010.05.004
4540:Kelso, J. A. Scott (1995).
3895:10.1088/0953-8984/18/50/007
3465:10.1088/0953-8984/18/49/L02
2962:Faghri, A., and Zhang, Y.,
2947:Faghri, A., and Zhang, Y.,
2831:Pippard, Alfred B. (1981).
2716:. Oxford University Press.
2714:Concepts in Thermal Physics
2380:
2208:static universality classes
2004:from a normal state to the
1677:
1514:decay of correlations near
473:
408:
10:
5647:
5014:Statistical Physics Part 1
4657:10.1103/PhysRevE.75.011920
4579:10.1037/0096-1523.21.1.183
4062:10.1103/PhysRevD.60.085001
4009:10.1103/PhysRevB.68.174518
3856:, Oxford Univ. Press, 1991
3824:Chaisson, Eric J. (2001).
3789:Pure and Applied Chemistry
3706:10.1103/PhysRevB.80.174413
3568:10.1103/PhysRevB.74.012403
3404:10.1103/PhysRevB.64.104416
3046:10.1103/PhysRevB.73.184435
2937:. Oxford: Clarendon Press.
2307:
1822:
910:Spin gapless semiconductor
633:Bose–Einstein condensation
412:
390:martensitic transformation
334:
124:
5527:
5481:
5353:
5267:
5241:
5185:
5174:
5136:
4834:10.1103/revmodphys.46.597
4395:10.1007/s10955-011-0229-4
1809:relational order theories
1611:Characteristic properties
1578:quantum phase transitions
1467:are those that involve a
1394:thermodynamic free energy
850:Electronic band structure
682:quantum phase transitions
670:thermodynamic free energy
662:equilibrium fractionation
518:, or they have different
104:Types of phase transition
5600:Thermo-dielectric effect
5499:Enthalpy of vaporization
5193:Bose–Einstein condensate
3000:10.1103/physrevb.19.3580
2479:List of states of matter
2352:tantalum hafnium carbide
2316:peace and armed conflict
1791:electroweak baryogenesis
1584:, belong to this class.
1444:, discovered in 1944 by
1385:Ehrenfest classification
760:Bose–Einstein condensate
691:Condensed matter physics
627:Quantum condensation of
5494:Enthalpy of sublimation
4422:Physical Review Letters
4331:10.1073/pnas.1324186111
4262:10.1073/pnas.1324045111
3802:10.1351/pac199466030577
3077:Physical Review Letters
2751:10.1103/PhysRevD.21.446
2228:coil-globule transition
1986:{\displaystyle \gamma }
1589:liquid–glass transition
1572:in the two-dimensional
1419:magnetic susceptibility
5509:Latent internal energy
5259:Color-glass condensate
4602:Human Movement Science
4085:J. Biomol. Struct. Dyn
2337:Mössbauer spectroscopy
2145:
1987:
1937:
1773:Relevance in cosmology
1723:will usually diverge.
1528:Type-II superconductor
1457:Modern classifications
648:breaking of symmetries
643:is an example of this.
602:The dependence of the
584:
558:spinodal decomposition
499:
432:
429:Manganese monosilicide
373:. The change from one
362:
122:
37:
5319:Magnetically ordered
5077:at Wikimedia Commons
5029:Schroeder, Manfred R.
4805:Switzerland AG, 2020.
4165:YashRoy, R C (1990).
2909:10.1007/s004070050021
2688:10.1007/s004070050021
2567:Nature Communications
2409:Abnormal grain growth
2204:enhanced fluctuations
2196:critical slowing down
2175:renormalization group
2146:
1988:
1938:
1787:electromagnetic field
1700:accidental symmetries
1524:Type-I superconductor
905:Topological insulator
654:Isotope fractionation
639:transition in liquid
578:
481:
422:
344:
116:
76:, and in rare cases,
35:
5198:Fermionic condensate
5088:Universality classes
4945:on 26 February 2008.
4854:, Berlin: Springer,
3738:Complex Nonlinearity
3149:J. Non-Cryst. Solids
2247:biological membranes
2212:dynamic universality
2073:
1977:
1885:
1870:, the heat capacity
1692:translation symmetry
1672:critical opalescence
1591:is observed in many
1555:multicritical points
923:Electronic phenomena
770:Fermionic condensate
82:thermodynamic system
5413:Chemical ionization
5305:Programmable matter
5295:Quantum spin liquid
5163:Supercritical fluid
4973:1974PhR....12...75W
4902:", pp. 1–742,
4898:; Disorder Fields,
4826:1974RvMP...46..597F
4706:2010PhyA..389.3193G
4649:2007PhRvE..75a1920M
4444:2014PhRvL.113f8102S
4387:2011JSP...144..268M
4322:2014PNAS..111.3683K
4253:2014PNAS..111.7212B
4126:Yashroy RC (1987).
4054:1999PhRvD..60h5001K
4001:2003PhRvB..68q4518L
3940:2015PhRvL.115t0601L
3887:2006JPCM...1811507O
3881:(50): 11507–11520.
3698:2009PhRvB..80q4413K
3629:2012JPCM...24L6004L
3560:2006PhRvB..74a2403R
3500:2006NatMa...5..881W
3457:2006JPCM...18L.605B
3396:2001PhRvB..64j4416M
3321:2007Natur.448..758T
3303:Tarjus, G. (2007).
3266:1995Sci...267.1947G
3260:(5206): 1947–1953.
3215:2007ARPC...58..235L
3161:2013JNCS..382...79O
3099:2008PhRvL.100x7003P
3038:2006PhRvB..73r4435K
2992:1979PhRvB..19.3580I
2870:10.1021/ie50275a006
2791:2014JSMTE..01..012M
2597:10.1038/ncomms10102
2589:2015NatCo...610102R
2435:Ehrenfest equations
2343:Neutron diffraction
2254:thylakoid membranes
930:Quantum Hall effect
425:magnetic structures
398:titanium aluminides
188:
86:physical properties
5631:Critical phenomena
5626:Physical phenomena
5560:Leidenfrost effect
5489:Enthalpy of fusion
5254:Quark–gluon plasma
4988:Krieger, Martin H.
4785:Perseus Publishing
2931:Stanley, H. Eugene
2491:Percolation theory
2485:Micro-pulling-down
2358:Raman Spectroscopy
2230:in the process of
2182:Critical phenomena
2141:
1983:
1933:
1842:correlation length
1838:critical exponents
1813:order and disorder
1690:breaks continuous
1508:correlation length
1327:Physics portal
585:
537:transformation. A
500:
433:
415:Magnetic structure
363:
351:crystal structures
347:allotropes of iron
157:
123:
38:
5621:Phase transitions
5608:
5607:
5590:Superheated vapor
5585:Superconductivity
5555:Equation of state
5403:Flash evaporation
5355:Phase transitions
5340:String-net liquid
5233:Photonic molecule
5203:Degenerate matter
5084:with Java applets
5073:Media related to
4900:Phase Transitions
4861:978-3-540-79356-4
4690:(16): 3193–3217.
4637:Physical Review E
4551:978-0-262-61131-2
4306:(10): 3683–3688.
4237:(20): 7212–7217.
4032:Physical Review D
3979:Physical Review B
3839:978-0-674-00342-2
3748:978-3-540-79357-1
3676:Physical Review B
3548:Physical Review B
3374:Physical Review B
3315:(7155): 758–759.
3016:Physical Review B
2864:(11): 1225–1235.
2842:978-0-521-09101-5
2739:Physical Review D
2723:978-0-19-856770-7
2547:978-0-412-53910-7
2449:Jamming (physics)
2375:X-ray diffraction
2192:critical dynamics
2002:lambda transition
1906:
1825:critical exponent
1783:electroweak field
1704:virtual particles
1688:crystalline solid
1684:symmetry breaking
1616:Phase coexistence
1603:quenched disorder
1488:quenched disorder
1415:Curie temperature
1377:
1376:
1075:Granular material
843:Electronic phases
620:The emergence of
615:superconductivity
613:The emergence of
516:congruent melting
437:magnetic ordering
375:crystal structure
297:
296:
159:Phase transitions
16:(Redirected from
5638:
5545:Compressed fluid
5180:
5125:States of matter
5118:
5111:
5104:
5095:
5094:
5072:
4984:
4946:
4941:. Archived from
4871:
4870:
4868:
4840:Goldenfeld, N.,
4837:
4765:
4764:
4762:
4743:
4732:
4726:
4725:
4699:
4675:
4669:
4668:
4632:
4626:
4625:
4597:
4591:
4590:
4562:
4556:
4555:
4537:
4531:
4530:
4504:
4480:
4474:
4473:
4463:
4437:
4413:
4407:
4406:
4380:
4360:
4354:
4353:
4343:
4333:
4315:
4291:
4285:
4284:
4274:
4264:
4246:
4222:
4216:
4215:
4213:
4201:
4195:
4194:
4162:
4156:
4155:
4123:
4117:
4116:
4080:
4074:
4073:
4047:
4027:
4021:
4020:
3994:
3992:cond-mat/0310163
3974:
3968:
3967:
3933:
3913:
3907:
3906:
3872:
3863:
3857:
3850:
3844:
3843:
3831:
3828:Cosmic Evolution
3821:
3815:
3814:
3804:
3780:
3774:
3773:
3767:
3759:
3757:
3755:
3732:
3726:
3725:
3691:
3671:
3665:
3664:
3622:
3586:
3580:
3579:
3534:
3528:
3527:
3508:10.1038/nmat1743
3488:Nature Materials
3483:
3477:
3476:
3450:
3448:cond-mat/0611152
3430:
3424:
3423:
3389:
3387:cond-mat/0012472
3357:
3351:
3350:
3332:
3300:
3294:
3293:
3249:
3243:
3242:
3208:
3206:cond-mat/0607349
3188:
3182:
3179:
3173:
3172:
3144:
3135:
3134:
3092:
3072:
3066:
3065:
3031:
3029:cond-mat/0602627
3010:
3004:
3003:
2986:(7): 3580–3585.
2975:
2969:
2960:
2954:
2945:
2939:
2938:
2927:
2921:
2920:
2888:
2882:
2881:
2853:
2847:
2846:
2828:
2819:
2818:
2784:
2760:
2754:
2753:
2734:
2728:
2727:
2709:
2700:
2699:
2671:
2662:
2661:
2659:
2657:
2642:
2636:
2634:, Elsevier, 2019
2625:
2619:
2618:
2608:
2582:
2558:
2552:
2551:
2533:
2475:
2454:
2445:
2431:
2414:
2399:
2369:Thermogravimetry
2240:DNA condensation
2188:static functions
2150:
2148:
2147:
2142:
2122:
2089:
1992:
1990:
1989:
1984:
1942:
1940:
1939:
1934:
1929:
1928:
1920:
1908:
1907:
1904:
1898:
1874:typically has a
1710:Order parameters
1545:phenomenological
1502:are also called
1499:
1498:
1369:
1362:
1355:
1342:
1337:
1336:
1329:
1325:
1324:
935:Spin Hall effect
825:Phase transition
795:Luttinger liquid
732:States of matter
715:Phase transition
701:
687:
686:
591:Transition to a
189:
182:
175:
168:
156:
137:states of matter
109:States of matter
62:states of matter
58:physical process
50:phase transition
21:
5646:
5645:
5641:
5640:
5639:
5637:
5636:
5635:
5611:
5610:
5609:
5604:
5535:Baryonic matter
5523:
5477:
5448:Saturated fluid
5388:Crystallization
5349:
5323:Antiferromagnet
5263:
5237:
5181:
5172:
5132:
5122:
5066:
4949:readable online
4939:
4923:Kleinert, Hagen
4866:
4864:
4862:
4803:Springer Nature
4773:
4771:Further reading
4768:
4760:
4741:
4733:
4729:
4676:
4672:
4633:
4629:
4598:
4594:
4563:
4559:
4552:
4538:
4534:
4481:
4477:
4414:
4410:
4361:
4357:
4292:
4288:
4223:
4219:
4202:
4198:
4163:
4159:
4124:
4120:
4081:
4077:
4028:
4024:
3975:
3971:
3918:Phys. Rev. Lett
3914:
3910:
3870:
3864:
3860:
3851:
3847:
3840:
3822:
3818:
3781:
3777:
3761:
3760:
3753:
3751:
3749:
3733:
3729:
3672:
3668:
3604:
3600:
3596:
3592:
3587:
3583:
3545:
3541:
3535:
3531:
3494:(11): 881–886.
3484:
3480:
3431:
3427:
3371:
3367:
3363:
3358:
3354:
3330:10.1038/448758a
3301:
3297:
3250:
3246:
3189:
3185:
3180:
3176:
3145:
3138:
3073:
3069:
3011:
3007:
2976:
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2961:
2957:
2946:
2942:
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2924:
2889:
2885:
2854:
2850:
2843:
2829:
2822:
2761:
2757:
2735:
2731:
2724:
2710:
2703:
2672:
2665:
2655:
2653:
2643:
2639:
2626:
2622:
2559:
2555:
2548:
2534:
2530:
2526:
2521:
2504:Superfluid film
2473:
2452:
2443:
2429:
2412:
2397:
2383:
2324:
2312:
2306:
2277:neural networks
2232:protein folding
2226:formation, the
2220:
2184:
2118:
2085:
2074:
2071:
2070:
1978:
1975:
1974:
1921:
1916:
1915:
1903:
1899:
1894:
1886:
1883:
1882:
1869:
1858:
1827:
1821:
1775:
1755:superconducting
1716:order parameter
1712:
1680:
1664:
1662:Critical points
1657:
1650:
1642:
1634:
1627:
1618:
1613:
1539:measurements.
1496:
1495:
1459:
1427:Cornelis Gorter
1407:order parameter
1387:
1382:
1380:Classifications
1373:
1332:
1319:
1318:
1311:
1310:
1309:
1099:
1091:
1090:
1089:
1065:Amorphous solid
1059:
1049:
1048:
1047:
1026:
1008:
998:
997:
996:
985:
983:Antiferromagnet
976:
974:Superparamagnet
967:
954:
953:Magnetic phases
946:
945:
944:
924:
916:
915:
914:
844:
836:
835:
834:
820:Order parameter
814:
813:Phase phenomena
806:
805:
804:
734:
724:
672:of a system is
573:
565:supersaturation
551:miscibility gap
524:solid solutions
476:
417:
411:
379:amorphous solid
339:
333:
311:(as opposed to
197:
194:
186:
133:
111:
106:
80:. A phase of a
28:
23:
22:
15:
12:
11:
5:
5644:
5634:
5633:
5628:
5623:
5606:
5605:
5603:
5602:
5597:
5592:
5587:
5582:
5577:
5572:
5567:
5562:
5557:
5552:
5547:
5542:
5537:
5531:
5529:
5525:
5524:
5522:
5521:
5516:
5514:Trouton's rule
5511:
5506:
5501:
5496:
5491:
5485:
5483:
5479:
5478:
5476:
5475:
5470:
5465:
5460:
5455:
5450:
5445:
5440:
5435:
5430:
5425:
5420:
5415:
5410:
5405:
5400:
5395:
5390:
5385:
5383:Critical point
5380:
5375:
5370:
5365:
5359:
5357:
5351:
5350:
5348:
5347:
5342:
5337:
5336:
5335:
5330:
5325:
5317:
5312:
5307:
5302:
5297:
5292:
5287:
5285:Liquid crystal
5282:
5277:
5271:
5269:
5265:
5264:
5262:
5261:
5256:
5251:
5245:
5243:
5239:
5238:
5236:
5235:
5230:
5225:
5220:
5218:Strange matter
5215:
5213:Rydberg matter
5210:
5205:
5200:
5195:
5189:
5187:
5183:
5182:
5175:
5173:
5171:
5170:
5165:
5160:
5151:
5146:
5140:
5138:
5134:
5133:
5121:
5120:
5113:
5106:
5098:
5092:
5091:
5090:from Sklogwiki
5085:
5065:
5064:External links
5062:
5061:
5060:
5050:
5040:
5026:
5023:
5010:Lifshitz, E.M.
5003:
4985:
4952:
4937:
4919:
4881:
4872:
4860:
4845:
4838:
4820:(4): 597–616.
4814:Rev. Mod. Phys
4806:
4788:
4777:Anderson, P.W.
4772:
4769:
4767:
4766:
4727:
4670:
4627:
4608:(4): 483–493.
4592:
4573:(1): 183–202.
4557:
4550:
4532:
4495:(2): 340–347.
4475:
4408:
4371:(2): 268–302.
4355:
4286:
4217:
4196:
4177:(4): 353–356.
4157:
4138:(6): 177–178.
4118:
4091:(5): 903–911.
4075:
4045:hep-th/9812197
4022:
3985:(17): 174518.
3969:
3924:(20): 200601.
3908:
3858:
3852:David Layzer,
3845:
3838:
3816:
3795:(3): 577–594.
3775:
3747:
3727:
3682:(17): 174413.
3666:
3613:(38): 386004.
3602:
3598:
3594:
3590:
3581:
3543:
3539:
3529:
3478:
3425:
3380:(10): 104416.
3369:
3365:
3361:
3352:
3295:
3244:
3183:
3174:
3136:
3083:(24): 247003.
3067:
3022:(18): 184435.
3005:
2970:
2955:
2940:
2922:
2883:
2848:
2841:
2820:
2755:
2745:(2): 446–453,
2729:
2722:
2701:
2663:
2637:
2620:
2553:
2546:
2527:
2525:
2522:
2520:
2519:
2513:
2507:
2501:
2500:
2499:
2488:
2482:
2476:
2467:
2461:
2455:
2446:
2437:
2432:
2423:
2417:
2416:
2415:
2403:Crystal growth
2400:
2391:
2384:
2382:
2379:
2378:
2377:
2372:
2366:
2360:
2355:
2354:4215 °C.)
2345:
2340:
2334:
2323:
2320:
2305:
2302:
2259:linolenic acid
2219:
2216:
2190:there is also
2183:
2180:
2152:
2151:
2140:
2137:
2134:
2131:
2128:
2125:
2121:
2117:
2114:
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2107:
2104:
2101:
2098:
2095:
2092:
2088:
2084:
2081:
2078:
1982:
1944:
1943:
1932:
1927:
1924:
1919:
1914:
1911:
1902:
1897:
1893:
1890:
1867:
1856:
1823:Main article:
1820:
1817:
1774:
1771:
1721:susceptibility
1711:
1708:
1679:
1676:
1668:critical point
1663:
1660:
1655:
1648:
1640:
1632:
1625:
1617:
1614:
1612:
1609:
1478:, but forms a
1458:
1455:
1390:Paul Ehrenfest
1386:
1383:
1381:
1378:
1375:
1374:
1372:
1371:
1364:
1357:
1349:
1346:
1345:
1344:
1343:
1330:
1313:
1312:
1308:
1307:
1302:
1297:
1292:
1287:
1282:
1277:
1272:
1267:
1262:
1257:
1252:
1247:
1242:
1237:
1232:
1227:
1222:
1217:
1212:
1207:
1202:
1197:
1192:
1187:
1182:
1177:
1172:
1167:
1162:
1157:
1152:
1147:
1142:
1137:
1132:
1127:
1122:
1117:
1112:
1107:
1101:
1100:
1097:
1096:
1093:
1092:
1088:
1087:
1082:
1080:Liquid crystal
1077:
1072:
1067:
1061:
1060:
1055:
1054:
1051:
1050:
1046:
1045:
1040:
1035:
1030:
1021:
1016:
1010:
1009:
1006:Quasiparticles
1004:
1003:
1000:
999:
995:
994:
989:
980:
971:
965:Superdiamagnet
962:
956:
955:
952:
951:
948:
947:
943:
942:
937:
932:
926:
925:
922:
921:
918:
917:
913:
912:
907:
902:
897:
892:
890:Thermoelectric
887:
885:Superconductor
882:
877:
872:
867:
865:Mott insulator
862:
857:
852:
846:
845:
842:
841:
838:
837:
833:
832:
827:
822:
816:
815:
812:
811:
808:
807:
803:
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797:
792:
787:
782:
777:
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767:
762:
757:
752:
747:
742:
736:
735:
730:
729:
726:
725:
723:
722:
717:
712:
706:
703:
702:
694:
693:
666:
665:
660:condenses (an
651:
644:
625:
618:
611:
610:on iron (110).
600:
597:liquid crystal
572:
571:Other examples
569:
475:
472:
461:incommensurate
410:
407:
332:
329:
305:freezing point
295:
294:
292:
287:
285:
283:
279:
278:
273:
271:
266:
261:
257:
256:
254:
249:
247:
242:
238:
237:
235:
230:
225:
223:
219:
218:
213:
208:
203:
198:
195:
192:
185:
184:
177:
170:
162:
127:vapor pressure
110:
107:
105:
102:
26:
9:
6:
4:
3:
2:
5643:
5632:
5629:
5627:
5624:
5622:
5619:
5618:
5616:
5601:
5598:
5596:
5593:
5591:
5588:
5586:
5583:
5581:
5578:
5576:
5573:
5571:
5570:Mpemba effect
5568:
5566:
5563:
5561:
5558:
5556:
5553:
5551:
5550:Cooling curve
5548:
5546:
5543:
5541:
5538:
5536:
5533:
5532:
5530:
5526:
5520:
5517:
5515:
5512:
5510:
5507:
5505:
5502:
5500:
5497:
5495:
5492:
5490:
5487:
5486:
5484:
5480:
5474:
5473:Vitrification
5471:
5469:
5466:
5464:
5461:
5459:
5456:
5454:
5451:
5449:
5446:
5444:
5441:
5439:
5438:Recombination
5436:
5434:
5433:Melting point
5431:
5429:
5426:
5424:
5421:
5419:
5416:
5414:
5411:
5409:
5406:
5404:
5401:
5399:
5396:
5394:
5391:
5389:
5386:
5384:
5381:
5379:
5378:Critical line
5376:
5374:
5371:
5369:
5368:Boiling point
5366:
5364:
5361:
5360:
5358:
5356:
5352:
5346:
5343:
5341:
5338:
5334:
5331:
5329:
5326:
5324:
5321:
5320:
5318:
5316:
5313:
5311:
5308:
5306:
5303:
5301:
5300:Exotic matter
5298:
5296:
5293:
5291:
5288:
5286:
5283:
5281:
5278:
5276:
5273:
5272:
5270:
5266:
5260:
5257:
5255:
5252:
5250:
5247:
5246:
5244:
5240:
5234:
5231:
5229:
5226:
5224:
5221:
5219:
5216:
5214:
5211:
5209:
5206:
5204:
5201:
5199:
5196:
5194:
5191:
5190:
5188:
5184:
5179:
5169:
5166:
5164:
5161:
5159:
5155:
5152:
5150:
5147:
5145:
5142:
5141:
5139:
5135:
5130:
5126:
5119:
5114:
5112:
5107:
5105:
5100:
5099:
5096:
5089:
5086:
5083:
5080:
5079:
5078:
5076:
5075:Phase changes
5071:
5058:
5054:
5053:Yeomans J. M.
5051:
5048:
5044:
5043:H. E. Stanley
5041:
5038:
5037:W. H. Freeman
5034:
5030:
5027:
5024:
5021:
5020:
5015:
5011:
5007:
5004:
5001:
4997:
4993:
4989:
4986:
4982:
4978:
4974:
4970:
4967:(2): 75–199.
4966:
4962:
4958:
4953:
4950:
4944:
4940:
4938:981-02-4659-5
4934:
4930:
4929:
4924:
4920:
4917:
4913:
4912:9971-5-0210-0
4909:
4905:
4901:
4897:
4893:
4892:Superfluidity
4889:
4885:
4882:
4880:
4878:
4873:
4863:
4857:
4853:
4852:
4846:
4843:
4839:
4835:
4831:
4827:
4823:
4819:
4815:
4811:
4807:
4804:
4800:
4796:
4792:
4789:
4786:
4782:
4778:
4775:
4774:
4759:
4755:
4751:
4747:
4740:
4739:
4731:
4723:
4719:
4715:
4711:
4707:
4703:
4698:
4693:
4689:
4685:
4681:
4674:
4666:
4662:
4658:
4654:
4650:
4646:
4643:(1): 011920.
4642:
4638:
4631:
4623:
4619:
4615:
4611:
4607:
4603:
4596:
4588:
4584:
4580:
4576:
4572:
4568:
4561:
4553:
4547:
4544:. MIT Press.
4543:
4536:
4528:
4524:
4520:
4516:
4512:
4508:
4503:
4498:
4494:
4490:
4486:
4479:
4471:
4467:
4462:
4457:
4453:
4449:
4445:
4441:
4436:
4431:
4428:(6): 068102.
4427:
4423:
4419:
4412:
4404:
4400:
4396:
4392:
4388:
4384:
4379:
4374:
4370:
4366:
4359:
4351:
4347:
4342:
4337:
4332:
4327:
4323:
4319:
4314:
4309:
4305:
4301:
4297:
4290:
4282:
4278:
4273:
4268:
4263:
4258:
4254:
4250:
4245:
4240:
4236:
4232:
4228:
4221:
4212:
4207:
4200:
4192:
4188:
4184:
4180:
4176:
4172:
4168:
4161:
4153:
4149:
4145:
4141:
4137:
4133:
4129:
4122:
4114:
4110:
4106:
4102:
4098:
4094:
4090:
4086:
4079:
4071:
4067:
4063:
4059:
4055:
4051:
4046:
4041:
4038:(8): 085001.
4037:
4033:
4026:
4018:
4014:
4010:
4006:
4002:
3998:
3993:
3988:
3984:
3980:
3973:
3965:
3961:
3957:
3953:
3949:
3945:
3941:
3937:
3932:
3927:
3923:
3919:
3912:
3904:
3900:
3896:
3892:
3888:
3884:
3880:
3876:
3869:
3862:
3855:
3849:
3841:
3835:
3830:
3829:
3820:
3812:
3808:
3803:
3798:
3794:
3790:
3786:
3779:
3771:
3765:
3750:
3744:
3740:
3739:
3731:
3723:
3719:
3715:
3711:
3707:
3703:
3699:
3695:
3690:
3685:
3681:
3677:
3670:
3662:
3658:
3654:
3650:
3646:
3642:
3638:
3634:
3630:
3626:
3621:
3616:
3612:
3608:
3585:
3577:
3573:
3569:
3565:
3561:
3557:
3554:(1): 012403.
3553:
3549:
3533:
3525:
3521:
3517:
3513:
3509:
3505:
3501:
3497:
3493:
3489:
3482:
3474:
3470:
3466:
3462:
3458:
3454:
3449:
3444:
3440:
3436:
3429:
3421:
3417:
3413:
3409:
3405:
3401:
3397:
3393:
3388:
3383:
3379:
3375:
3356:
3348:
3344:
3340:
3336:
3331:
3326:
3322:
3318:
3314:
3310:
3306:
3299:
3291:
3287:
3283:
3279:
3275:
3271:
3267:
3263:
3259:
3255:
3248:
3240:
3236:
3232:
3228:
3224:
3220:
3216:
3212:
3207:
3202:
3198:
3194:
3187:
3178:
3170:
3166:
3162:
3158:
3154:
3150:
3143:
3141:
3132:
3128:
3124:
3120:
3116:
3112:
3108:
3104:
3100:
3096:
3091:
3086:
3082:
3078:
3071:
3063:
3059:
3055:
3051:
3047:
3043:
3039:
3035:
3030:
3025:
3021:
3017:
3009:
3001:
2997:
2993:
2989:
2985:
2981:
2974:
2967:
2966:
2959:
2952:
2951:
2944:
2936:
2932:
2926:
2918:
2914:
2910:
2906:
2902:
2898:
2894:
2887:
2879:
2875:
2871:
2867:
2863:
2859:
2852:
2844:
2838:
2834:
2827:
2825:
2816:
2812:
2808:
2804:
2800:
2796:
2792:
2788:
2783:
2778:
2775:(1): P01012.
2774:
2770:
2766:
2759:
2752:
2748:
2744:
2740:
2733:
2725:
2719:
2715:
2708:
2706:
2697:
2693:
2689:
2685:
2681:
2677:
2670:
2668:
2651:
2647:
2646:Carol Kendall
2641:
2635:
2632:
2631:
2624:
2616:
2612:
2607:
2602:
2598:
2594:
2590:
2586:
2581:
2576:
2572:
2568:
2564:
2557:
2549:
2543:
2539:
2532:
2528:
2517:
2514:
2511:
2508:
2505:
2502:
2498:
2495:
2494:
2492:
2489:
2486:
2483:
2480:
2477:
2471:
2468:
2465:
2464:Landau theory
2462:
2459:
2456:
2450:
2447:
2441:
2438:
2436:
2433:
2427:
2424:
2421:
2418:
2410:
2407:
2406:
2404:
2401:
2395:
2392:
2389:
2386:
2385:
2376:
2373:
2371:(very common)
2370:
2367:
2364:
2361:
2359:
2356:
2353:
2349:
2346:
2344:
2341:
2338:
2335:
2332:
2329:
2328:
2327:
2319:
2317:
2311:
2301:
2297:
2294:
2290:
2286:
2281:
2278:
2273:
2271:
2267:
2264:
2260:
2255:
2252:
2248:
2243:
2241:
2237:
2233:
2229:
2225:
2224:lipid bilayer
2215:
2213:
2209:
2205:
2201:
2197:
2193:
2189:
2179:
2176:
2170:
2168:
2163:
2161:
2157:
2138:
2132:
2129:
2126:
2119:
2115:
2112:
2109:
2105:
2099:
2096:
2093:
2086:
2082:
2079:
2076:
2069:
2068:
2067:
2065:
2061:
2057:
2053:
2049:
2044:
2042:
2036:
2034:
2030:
2026:
2022:
2017:
2015:
2011:
2007:
2003:
1999:
1994:
1980:
1970:
1968:
1964:
1961:The exponent
1959:
1957:
1953:
1949:
1930:
1925:
1922:
1912:
1909:
1900:
1891:
1888:
1881:
1880:
1879:
1877:
1873:
1866:
1862:
1855:
1851:
1847:
1846:heat capacity
1843:
1839:
1834:
1832:
1826:
1816:
1814:
1810:
1805:
1803:
1799:
1798:Eric Chaisson
1794:
1792:
1788:
1784:
1780:
1770:
1768:
1764:
1759:
1756:
1751:
1749:
1745:
1744:magnetization
1741:
1740:ferromagnetic
1735:
1733:
1732:ferromagnetic
1729:
1728:magnetization
1724:
1722:
1717:
1707:
1705:
1701:
1697:
1693:
1689:
1685:
1675:
1673:
1669:
1659:
1654:
1647:
1639:
1631:
1624:
1608:
1605:
1604:
1598:
1594:
1590:
1585:
1583:
1579:
1575:
1571:
1567:
1563:
1558:
1556:
1551:
1549:
1546:
1542:
1538:
1533:
1529:
1525:
1521:
1520:ferromagnetic
1517:
1513:
1509:
1505:
1501:
1492:
1489:
1485:
1481:
1477:
1472:
1470:
1466:
1462:
1454:
1451:
1447:
1443:
1438:
1436:
1430:
1428:
1422:
1420:
1416:
1412:
1411:magnetization
1408:
1404:
1399:
1395:
1391:
1370:
1365:
1363:
1358:
1356:
1351:
1350:
1348:
1347:
1341:
1331:
1328:
1323:
1317:
1316:
1315:
1314:
1306:
1303:
1301:
1298:
1296:
1293:
1291:
1288:
1286:
1283:
1281:
1278:
1276:
1273:
1271:
1268:
1266:
1263:
1261:
1258:
1256:
1253:
1251:
1248:
1246:
1243:
1241:
1238:
1236:
1233:
1231:
1228:
1226:
1223:
1221:
1218:
1216:
1213:
1211:
1208:
1206:
1203:
1201:
1198:
1196:
1193:
1191:
1188:
1186:
1183:
1181:
1178:
1176:
1173:
1171:
1168:
1166:
1163:
1161:
1158:
1156:
1153:
1151:
1148:
1146:
1143:
1141:
1138:
1136:
1133:
1131:
1128:
1126:
1123:
1121:
1118:
1116:
1113:
1111:
1108:
1106:
1105:Van der Waals
1103:
1102:
1095:
1094:
1086:
1083:
1081:
1078:
1076:
1073:
1071:
1068:
1066:
1063:
1062:
1058:
1053:
1052:
1044:
1041:
1039:
1036:
1034:
1031:
1029:
1025:
1022:
1020:
1017:
1015:
1012:
1011:
1007:
1002:
1001:
993:
990:
988:
984:
981:
979:
975:
972:
970:
966:
963:
961:
958:
957:
950:
949:
941:
938:
936:
933:
931:
928:
927:
920:
919:
911:
908:
906:
903:
901:
900:Ferroelectric
898:
896:
895:Piezoelectric
893:
891:
888:
886:
883:
881:
878:
876:
873:
871:
870:Semiconductor
868:
866:
863:
861:
858:
856:
853:
851:
848:
847:
840:
839:
831:
828:
826:
823:
821:
818:
817:
810:
809:
801:
798:
796:
793:
791:
790:Superfluidity
788:
786:
783:
781:
778:
776:
773:
771:
768:
766:
763:
761:
758:
756:
753:
751:
748:
746:
743:
741:
738:
737:
733:
728:
727:
721:
718:
716:
713:
711:
708:
707:
705:
704:
700:
696:
695:
692:
689:
688:
685:
683:
679:
675:
671:
663:
659:
655:
652:
649:
645:
642:
638:
634:
630:
626:
623:
619:
616:
612:
609:
605:
601:
598:
594:
590:
589:
588:
582:
577:
568:
566:
561:
559:
554:
552:
548:
544:
540:
536:
532:
527:
525:
521:
517:
513:
512:melting point
509:
505:
497:
493:
492:mixing ratios
490:at different
489:
485:
480:
471:
470:
466:
462:
458:
454:
450:
446:
442:
441:ferromagnetic
438:
430:
426:
421:
416:
406:
403:
399:
395:
391:
386:
384:
380:
376:
372:
368:
360:
357:(α-iron) and
356:
352:
348:
343:
338:
328:
326:
322:
318:
314:
313:adiabatically
310:
306:
302:
301:phase diagram
293:
291:
290:Recombination
288:
281:
280:
277:
274:
272:
270:
267:
265:
262:
259:
258:
253:
250:
248:
246:
243:
240:
239:
234:
231:
229:
226:
224:
221:
220:
217:
214:
212:
209:
207:
204:
202:
199:
191:
190:
183:
178:
176:
171:
169:
164:
163:
160:
155:
153:
148:
146:
142:
141:boiling point
138:
132:
131:phase diagram
128:
120:
115:
101:
99:
98:boiling point
95:
91:
87:
83:
79:
75:
71:
67:
63:
59:
55:
51:
47:
43:
34:
30:
19:
5595:Superheating
5468:Vaporization
5463:Triple point
5458:Supercooling
5423:Lambda point
5373:Condensation
5290:Time crystal
5268:Other states
5208:Quantum Hall
5067:
5056:
5046:
5035:, New York:
5032:
5017:
5016:, vol. 5 of
5013:
5006:Landau, L.D.
4991:
4964:
4960:
4943:the original
4927:
4906:; Paperback
4896:Vortex lines
4887:
4884:Kleinert, H.
4876:
4865:, retrieved
4850:
4841:
4817:
4813:
4810:Fisher, M.E.
4780:
4737:
4730:
4687:
4683:
4673:
4640:
4636:
4630:
4605:
4601:
4595:
4570:
4566:
4560:
4541:
4535:
4492:
4488:
4478:
4425:
4421:
4411:
4368:
4364:
4358:
4303:
4299:
4289:
4234:
4230:
4220:
4199:
4174:
4170:
4160:
4135:
4131:
4121:
4088:
4084:
4078:
4035:
4031:
4025:
3982:
3978:
3972:
3921:
3917:
3911:
3878:
3874:
3861:
3853:
3848:
3827:
3819:
3792:
3788:
3778:
3752:. Retrieved
3737:
3730:
3679:
3675:
3669:
3610:
3606:
3584:
3551:
3547:
3532:
3491:
3487:
3481:
3441:(49): L605.
3438:
3434:
3428:
3377:
3373:
3355:
3312:
3308:
3298:
3257:
3253:
3247:
3196:
3192:
3186:
3177:
3152:
3148:
3080:
3076:
3070:
3019:
3015:
3008:
2983:
2980:Phys. Rev. B
2979:
2973:
2964:
2958:
2949:
2943:
2934:
2925:
2903:(1): 51–81.
2900:
2896:
2886:
2861:
2857:
2851:
2832:
2772:
2768:
2758:
2742:
2738:
2732:
2713:
2682:(1): 51–81.
2679:
2675:
2654:. Retrieved
2640:
2633:
2630:
2623:
2570:
2566:
2556:
2537:
2531:
2325:
2322:Experimental
2313:
2298:
2282:
2274:
2246:
2244:
2221:
2211:
2207:
2203:
2199:
2195:
2191:
2187:
2185:
2171:
2167:universality
2166:
2164:
2159:
2155:
2153:
2063:
2059:
2055:
2051:
2047:
2045:
2037:
2032:
2024:
2020:
2018:
2009:
1997:
1996:For −1 <
1995:
1971:
1966:
1962:
1960:
1955:
1951:
1947:
1945:
1871:
1864:
1860:
1853:
1849:
1835:
1828:
1806:
1802:David Layzer
1795:
1776:
1760:
1752:
1736:
1725:
1715:
1713:
1681:
1665:
1652:
1645:
1637:
1629:
1622:
1619:
1601:
1586:
1561:
1559:
1552:
1503:
1494:
1493:
1473:
1464:
1463:
1460:
1446:Lars Onsager
1439:
1431:
1423:
1402:
1397:
1388:
1235:von Klitzing
940:Kondo effect
824:
800:Time crystal
780:Fermi liquid
714:
674:non-analytic
667:
622:metamaterial
586:
562:
555:
528:
501:
496:temperatures
457:commensurate
445:paramagnetic
434:
387:
371:polymorphism
364:
325:supercooling
321:superheating
309:diabatically
298:
269:Condensation
252:Vaporization
158:
149:
134:
54:phase change
53:
49:
39:
29:
5504:Latent heat
5453:Sublimation
5398:Evaporation
5333:Ferromagnet
5328:Ferrimagnet
5310:Dark matter
5242:High energy
4955:Kogut, J.;
4890:, Vol. I, "
3199:: 235–266.
2440:Ising Model
2331:Hall effect
2293:hydrophilic
2251:chloroplast
2236:DNA melting
2200:speeding up
2041:logarithmic
2029:Ising model
2019:For 0 <
1954:instead of
1831:latent heat
1748:Curie point
1597:supercooled
1580:, e.g., in
1516:criticality
1484:Yoseph Imry
1469:latent heat
1442:Ising model
1057:Soft matter
978:Ferromagnet
658:water vapor
543:peritectoid
469:Ising Model
453:Curie point
383:polyamorphs
233:Sublimation
161:of matter (
90:temperature
5615:Categories
5519:Volatility
5482:Quantities
5443:Regelation
5418:Ionization
5393:Deposition
5345:Superglass
5315:Antimatter
5249:QCD matter
5228:Supersolid
5223:Superfluid
5186:Low energy
4791:Faghri, A.
4754:Q126669745
3931:1508.07852
3754:12 October
2580:1507.08901
2524:References
2308:See also:
2289:scale-free
2263:spin label
2035:≈ +0.110.
2006:superfluid
1878:behavior:
1566:symmetries
1541:Lev Landau
1532:superfluid
1450:mean-field
1200:Louis Néel
1190:Schrieffer
1098:Scientists
992:Spin glass
987:Metamagnet
969:Paramagnet
785:Supersolid
637:superfluid
604:adsorption
547:monotectic
539:peritectic
465:antimonide
447:phases of
413:See also:
402:metastable
353:including
335:See also:
331:Structural
317:metastable
276:Ionization
264:Deposition
125:See also:
4961:Phys. Rep
4957:Wilson, K
4795:Zhang, Y.
4697:0905.0129
4502:1103.1833
4435:1310.0448
4378:1012.2242
4313:1309.2614
4244:1307.5563
4211:1407.5946
4070:117436273
3764:cite book
3722:119165221
3714:1098-0121
3689:0911.4552
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2807:1742-5468
2782:1311.0580
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1807:See also
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1512:power law
1480:turbulent
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1195:Josephson
1165:Van Vleck
1155:Luttinger
1028:Polariton
960:Diamagnet
880:Conductor
875:Semimetal
860:Insulator
775:Fermi gas
599:" phases.
593:mesophase
535:eutectoid
504:solutions
367:allotropy
361:(γ-iron).
359:austenite
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5580:Spinodal
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4867:14 March
4758:archived
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245:Freezing
152:pressure
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