1127:
193:
272:
350:
534:, even if the renormalized mass is zero, spontaneous symmetry breaking still happens due to the radiative corrections (this introduces a mass scale into a classically conformal theory - the model has a
37:
664:
569:. There are non-minimal models that give a more realistic scenarios. Also the variations of this mechanism were proposed for the hypothetical spontaneously broken symmetries including
791:
829:
706:
622:
The three-dimensional version of the
Coleman–Weinberg model governs the superconducting phase transition which can be both first- and second-order, depending on the ratio of the
471:
426:
393:
741:
524:
605:
559:
491:
370:
936:
914:
719:. Historically, the order of the superconducting phase transition was debated for a long time since the temperature interval where fluctuations are large (
720:
201:
277:
755:) is large enough, vortex fluctuations becomes important which drive the transition to second order. The tricritical point lies at roughly
1192:
1168:
957:
565:, as a matter of fact even too light to explain the electroweak symmetry breaking in the minimal model - much lighter than
188:{\displaystyle L=-{\frac {1}{4}}(F_{\mu \nu })^{2}+|D_{\mu }\phi |^{2}-m^{2}|\phi |^{2}-{\frac {\lambda }{6}}|\phi |^{4}}
983:
628:
1197:
758:
1187:
623:
429:
1142:
796:
673:
1161:
752:
608:
541:
The same can happen in other gauge theories. In the broken phase the fluctuations of the scalar field
1065:
28:
1024:"Disorder Version of the Abelian Higgs Model and the Order of the Superconductive Phase Transition"
723:) is extremely small. The question was finally settled in 1982. If the Ginzburg–Landau parameter
24:
443:
398:
836:
832:
748:
713:
1066:"Vortex interactions and thermally induced crossover from type-I to type-II superconductivity"
378:
1154:
744:
726:
709:
496:
1090:
881:
583:
544:
476:
8:
999:
840:
1094:
885:
1106:
1080:
1046:
975:
897:
871:
355:
1134:
1050:
1023:
979:
953:
862:
716:
667:
612:
535:
1110:
1098:
1038:
945:
901:
889:
616:
577:
967:
927:
437:
949:
860:(1973). "Radiative Corrections as the Origin of Spontaneous Symmetry Breaking".
1138:
1102:
1019:
857:
853:
531:
527:
433:
267:{\displaystyle F_{\mu \nu }=\partial _{\mu }A_{\nu }-\partial _{\nu }A_{\mu }}
1181:
570:
893:
566:
1085:
562:
345:{\displaystyle D_{\mu }=\partial _{\mu }-\mathrm {i} (e/\hbar c)A_{\mu }}
1042:
931:
909:
876:
607:. The model is the four-dimensional analog of the three-dimensional
576:
Equivalently one may say that the model possesses a first-order
1126:
926:
493:
is zero. At the classical level the latter is true also if
852:
839:
superconductor. The prediction was confirmed in 2002 by
352:
the covariant derivative containing the electric charge
440:. On the other hand, if the squared mass is positive,
799:
761:
729:
676:
631:
586:
547:
499:
479:
446:
401:
381:
358:
280:
204:
40:
1063:
395:
is nonnegative. Then if the mass term is tachyonic,
912:(1937). "On the theory of phase transitions. II".
823:
785:
735:
700:
658:
599:
553:
518:
485:
465:
420:
387:
364:
344:
266:
187:
937:Zhurnal Eksperimental'noi i Teoreticheskoi Fiziki
915:Zhurnal Eksperimental'noi i Teoreticheskoi Fiziki
1179:
934:(1950). "On the theory of superconductivity".
561:will manifest themselves as a naturally light
1162:
659:{\displaystyle \kappa \equiv \lambda /e^{2}}
1018:
908:
1169:
1155:
27:of a scalar field in four-dimensions. The
1084:
974:. Dover Books on Physics (2nd ed.).
966:
875:
274:is the electromagnetic field tensor, and
786:{\displaystyle \kappa =0.76/{\sqrt {2}}}
1180:
824:{\displaystyle \kappa =1/{\sqrt {2}}}
701:{\displaystyle \kappa =1/{\sqrt {2}}}
1121:
473:the vacuum expectation of the field
198:where the scalar field is complex,
16:Potential arising from loop effects
13:
611:used to explain the properties of
436:at low energies, a variant of the
308:
295:
245:
222:
14:
1209:
1064:J. Hove; S. Mo; A. Sudbo (2002).
972:Introduction to Superconductivity
793:, i.e., slightly below the value
323:
1125:
841:Monte Carlo computer simulations
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1012:
372:of the electromagnetic field.
329:
312:
175:
166:
142:
133:
109:
90:
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60:
1:
1193:Quantum mechanical potentials
1005:
846:
1141:. You can help Knowledge by
7:
993:
950:10.1007/978-3-540-68008-6_4
526:. However, as was shown by
10:
1214:
1120:
1103:10.1103/PhysRevB.66.064524
751:superconductors (see also
466:{\displaystyle m^{2}>0}
421:{\displaystyle m^{2}<0}
624:Ginzburg–Landau parameter
1031:Lettere al Nuovo Cimento
388:{\displaystyle \lambda }
894:10.1103/PhysRevD.7.1888
736:{\displaystyle \kappa }
519:{\displaystyle m^{2}=0}
25:quantum electrodynamics
1137:-related article is a
825:
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702:
660:
609:Ginzburg–Landau theory
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520:
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21:Coleman–Weinberg model
1198:Quantum physics stubs
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600:{\displaystyle m^{2}}
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554:{\displaystyle \phi }
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486:{\displaystyle \phi }
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430:spontaneous breaking
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1095:2002PhRvB..66f4524H
1000:Quartic interaction
886:1973PhRvD...7.1888C
743:that distinguishes
1043:10.1007/BF02754760
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1135:quantum mechanics
959:978-3-540-68004-8
863:Physical Review D
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781:
721:Ginzburg interval
717:superconductivity
696:
668:tricritical point
580:as a function of
536:conformal anomaly
365:{\displaystyle e}
163:
58:
31:for the model is
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1086:cond-mat/0202215
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1016:
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923:
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870:(6): 1888–1910.
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815:
813:
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1037:(13): 405–412.
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835:goes over into
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1087:
1082:
1079:(6): 064524.
1078:
1074:
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1048:
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1040:
1036:
1032:
1025:
1021:
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987:
985:0-486-43503-2
981:
977:
973:
969:
965:
961:
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951:
947:
943:
939:
938:
933:
929:
928:V.L. Ginzburg
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921:
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642:
638:
635:
632:
625:
620:
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588:
579:
574:
572:
571:supersymmetry
568:
567:vector bosons
564:
548:
539:
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529:
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71:
68:
64:
55:
52:
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41:
34:
33:
32:
30:
26:
22:
1143:expanding it
1132:
1076:
1072:
1059:
1034:
1030:
1014:
971:
941:
935:
919:
913:
867:
861:
621:
575:
540:
375:Assume that
374:
197:
20:
18:
1020:H. Kleinert
944:: 113–137.
932:L.D. Landau
910:L.D. Landau
858:E. Weinberg
563:Higgs boson
428:there is a
23:represents
1182:Categories
1006:References
854:S. Coleman
847:Literature
29:Lagrangian
1073:Phys. Rev
1051:121012850
968:M.Tinkham
801:κ
763:κ
731:κ
678:κ
666:, with a
639:λ
636:≡
633:κ
615:near the
549:ϕ
481:ϕ
383:λ
338:μ
324:ℏ
305:−
300:μ
296:∂
287:μ
260:μ
250:ν
246:∂
242:−
237:ν
227:μ
223:∂
214:ν
211:μ
171:ϕ
158:λ
153:−
138:ϕ
120:−
105:ϕ
100:μ
72:ν
69:μ
48:−
1111:13672575
1022:(1982).
994:See also
970:(2004).
1091:Bibcode
902:6898114
882:Bibcode
837:type-II
749:type-II
714:type II
432:of the
1109:
1049:
982:
956:
922:: 627.
900:
833:type-I
831:where
745:type-I
710:type I
1133:This
1107:S2CID
1081:arXiv
1069:(PDF)
1047:S2CID
1027:(PDF)
976:Dover
898:S2CID
872:arXiv
747:and
712:from
670:near
1139:stub
1077:B 66
980:ISBN
954:ISBN
930:and
856:and
769:0.76
753:here
530:and
458:>
413:<
19:The
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946:doi
890:doi
538:).
1184::
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1035:35
1033:.
1029:.
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918:.
896:.
888:.
880:.
866:.
843:.
619:.
573:.
1170:e
1163:t
1156:v
1145:.
1113:.
1101::
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1041::
988:.
962:.
948::
920:7
904:.
892::
884::
874::
868:7
817:2
811:/
807:1
804:=
779:2
773:/
766:=
694:2
688:/
684:1
681:=
652:2
648:e
643:/
593:2
589:m
514:0
511:=
506:2
502:m
461:0
453:2
449:m
416:0
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404:m
360:e
334:A
330:)
327:c
320:/
316:e
313:(
309:i
292:=
283:D
256:A
233:A
219:=
207:F
181:4
176:|
167:|
161:6
148:2
143:|
134:|
128:2
124:m
115:2
110:|
96:D
91:|
87:+
82:2
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65:F
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42:L
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