Knowledge

Statistical field theory

Source đź“ť

575: 1711: 1662: 1607: 1652: 348: 1657: 898: 536: 1276: 1645: 1281: 891: 1005: 1640: 509: 378:
Baeurle SA, Nogovitsin EA (2007). "Challenging scaling laws of flexible polyelectrolyte solutions with effective renormalization concepts".
1458: 884: 591: 107: 1503: 596: 529: 60: 1010: 504: 1419: 1752: 1020: 522: 446: 331: 192: 1586: 1781: 1040: 1035: 347:
Baeurle SA, Usami T, Gusev AA (2006). "A new multiscale modeling approach for the prediction of mechanical properties of
167: 68: 488: 469: 429: 418: 1453: 1137: 1200: 960: 115: 1791: 1127: 790: 1786: 1776: 1132: 1025: 1771: 1686: 1030: 559: 48: 1072: 1745: 1690: 1154: 667: 583: 1550: 1483: 1478: 1441: 972: 945: 915: 80: 1407: 1311: 1271: 987: 843: 1726: 106:, many results of statistical field theory can be applied directly to its quantum equivalent. The 1596: 690: 680: 606: 1232: 1601: 1591: 1565: 1387: 1382: 1377: 1372: 1330: 1293: 1239: 965: 955: 933: 737: 1738: 1518: 1498: 1436: 1365: 1144: 1122: 1097: 997: 622: 545: 413:. Cambridge Monographs on Mathematical Physics. Vol. I, II. Cambridge University Press. 56: 1676: 1570: 1555: 1470: 1397: 1360: 1355: 1345: 1105: 1059: 765: 288: 227: 88: 72: 8: 1545: 1414: 1325: 1212: 1183: 907: 831: 810: 20: 292: 231: 1682: 1335: 1321: 1303: 1286: 1266: 1249: 1159: 982: 858: 770: 747: 728: 708: 672: 304: 278: 251: 217: 111: 1718: 1508: 1244: 1222: 1149: 1110: 1087: 876: 863: 760: 733: 644: 634: 627: 601: 484: 465: 442: 425: 414: 327: 308: 243: 208:
Rejmer, K.; Dietrich, S.; NapiĂłrkowski, M. (1999). "Filling transition for a wedge".
188: 163: 76: 40: 32: 255: 1426: 1217: 1205: 1188: 1166: 1115: 1067: 928: 755: 387: 360: 296: 235: 71:
of the system are expressed through field configurations. It is closely related to
805: 391: 364: 1532: 1488: 1315: 1259: 1254: 1193: 1015: 940: 800: 795: 723: 718: 685: 612: 436: 269:
Parry, A.O.; Rascon, C.; Wood, A.J. (1999). "Universality for 2D Wedge Wetting".
138: 122: 103: 99: 84: 64: 300: 35:. It does not denote a single theory but encompasses many models, including for 1722: 1176: 848: 564: 1765: 1493: 1448: 1431: 1077: 950: 836: 239: 95: 44: 1513: 1392: 1171: 1082: 977: 853: 247: 1624: 1540: 662: 657: 283: 222: 514: 1560: 652: 134: 126: 1608:
The Unreasonable Effectiveness of Mathematics in the Natural Sciences
923: 713: 36: 55:
as well as non-equilibrium phase transitions. A SFT is any model in
617: 121:
Statistical field theories are widely used to describe systems in
782: 130: 52: 1663:
European Community on Computational Methods in Applied Sciences
1227: 1045: 1710: 1658:
International Council for Industrial and Applied Mathematics
79:
of fields, and shares with it many techniques, such as the
207: 187:(2nd ed.). Cambridge: Cambridge University Press. 87:. If the system involves polymers, it is also known as 906: 1277:
Numerical methods for ordinary differential equations
1653:
Société de Mathématiques Appliquées et Industrielles
1646:
Japan Society for Industrial and Applied Mathematics
1282:
Numerical methods for partial differential equations
996: 481:
Quantum Physics: A Functional Integral Point of View
1469: 377: 346: 1763: 409:Itzykson, Claude; Drouffe, Jean-Michel (1991). 408: 268: 1641:Society for Industrial and Applied Mathematics 1746: 892: 530: 182: 1459:Supersymmetric theory of stochastic dynamics 114:, and their properties are described by the 31:) is a theoretical framework that describes 1753: 1739: 899: 885: 537: 523: 478: 544: 441:. Advanced Book Classics. Perseus Books. 326:. Cambridge: Cambridge University Press. 282: 221: 157: 110:of a statistical field theory are called 183:Altland, Alexander; Simons, Ben (2010). 510:Particle and Polymer Field Theory Group 16:Framework to describe phase transitions 1764: 434: 321: 880: 518: 455: 1705: 505:Problems in Statistical Field Theory 479:Glimm, James; Jaffe, Arthur (1987). 160:Quantum and Statistical Field Theory 13: 908:Industrial and applied mathematics 14: 1803: 1138:Stochastic differential equations 498: 1709: 1454:Supersymmetric quantum mechanics 573: 462:Euclidean (quantum) field theory 1336:Stochastic variational calculus 1128:Ordinary differential equations 67:or fields. In other words, the 1133:Partial differential equations 1006:Arbitrary-precision arithmetic 464:. Princeton University Press. 371: 340: 315: 262: 201: 176: 151: 1: 1021:Interactive geometry software 402: 392:10.1016/j.polymer.2007.05.080 365:10.1016/j.polymer.2006.10.017 185:Condensed Matter Field Theory 1725:. You can help Knowledge by 560:Principle of maximum entropy 133:films, nanostructured block 49:topological phase transition 7: 1073:Computational number theory 1036:Numerical-analysis software 349:polymer-based nanomaterials 301:10.1103/PhysRevLett.83.5535 162:. Oxford: Clarendon Press. 116:Osterwalder–Schrader axioms 10: 1808: 1782:Statistical field theories 1704: 584:Statistical thermodynamics 483:(2nd ed.). Springer. 158:Le Bellac, Michel (1991). 1671: 1633: 1617: 1579: 1531: 1479:Algebra of physical space 1344: 1302: 1096: 1058: 946:Automated theorem proving 914: 819: 781: 746: 701: 643: 582: 571: 552: 94:In fact, by performing a 81:path integral formulation 1272:Numerical linear algebra 844:Condensed matter physics 827:Statistical field theory 438:Statistical Field Theory 435:Parisi, Giorgio (1998). 411:Statistical Field Theory 240:10.1103/PhysRevE.60.4027 144: 25:statistical field theory 1011:Finite element analysis 961:Constraint satisfaction 702:Mathematical approaches 691:Lennard-Jones potential 607:thermodynamic potential 1721:-related article is a 1566:Mathematical economics 1240:Multivariable calculus 1123:Differential equations 966:Constraint programming 956:Computational geometry 738:conformal field theory 75:, which describes the 1792:Quantum physics stubs 1519:Supersymmetry algebra 1504:Representation theory 1499:Renormalization group 1145:Differential geometry 1026:Optimization software 998:Mathematical software 653:Ferromagnetism models 546:Statistical mechanics 456:Simon, Barry (1974). 108:correlation functions 57:statistical mechanics 1787:Quantum field theory 1777:Mathematical physics 1571:Mathematical finance 1556:Social choice theory 1471:Algebraic structures 1420:in quantum mechanics 1356:Analytical mechanics 1322:Stochastic processes 1294:Variational calculus 1106:Approximation theory 1031:Statistical software 322:Täuber, Uwe (2014). 89:polymer field theory 73:quantum field theory 1772:Applied mathematics 1546:Operations research 1415:Perturbation theory 1213:Multilinear algebra 1184:Functional analysis 1041:Numerical libraries 973:Computational logic 832:elementary particle 597:partition functions 293:1999PhRvL..83.5535P 232:1999PhRvE..60.4027R 112:Schwinger functions 21:theoretical physics 1683:Mathematics portal 1580:Other applications 1304:Probability theory 1287:Validated numerics 1267:Numerical analysis 1160:Geometric analysis 1150:Differential forms 983:Information theory 859:information theory 766:correlation length 761:Critical exponents 748:Critical phenomena 729:stochastic process 709:Boltzmann equation 602:equations of state 61:degrees of freedom 1734: 1733: 1719:quantum mechanics 1699: 1698: 1533:Decision sciences 1527: 1526: 1509:Spacetime algebra 1201:Harmonic analysis 1167:Dynamical systems 1111:Clifford analysis 1088:Discrete geometry 1054: 1053: 874: 873: 864:Boltzmann machine 734:mean-field theory 635:Maxwell relations 448:978-0-7382-0051-4 386:(16): 4883–4899. 359:(26): 8604–8617. 333:978-0-521-84223-5 324:Critical Dynamics 277:(26): 5535–5538. 194:978-0-521-76975-4 77:quantum mechanics 41:superconductivity 33:phase transitions 1799: 1755: 1748: 1741: 1713: 1706: 1484:Feynman integral 1467: 1466: 1427:Potential theory 1316:random variables 1206:Fourier analysis 1189:Operator algebra 1116:Clifford algebra 1068:Computer algebra 994: 993: 901: 894: 887: 878: 877: 756:Phase transition 577: 576: 539: 532: 525: 516: 515: 494: 475: 452: 424: 396: 395: 375: 369: 368: 344: 338: 337: 319: 313: 312: 286: 284:cond-mat/9912388 266: 260: 259: 225: 223:cond-mat/9812115 216:(4): 4027–4042. 205: 199: 198: 180: 174: 173: 155: 139:polyelectrolytes 1807: 1806: 1802: 1801: 1800: 1798: 1797: 1796: 1762: 1761: 1760: 1759: 1702: 1700: 1695: 1667: 1629: 1613: 1575: 1523: 1489:Poisson algebra 1465: 1347: 1340: 1298: 1194:Operator theory 1092: 1050: 1016:Tensor software 992: 941:Automata theory 910: 905: 875: 870: 815: 777: 742: 724:BBGKY hierarchy 719:Vlasov equation 697: 686:depletion force 679:Particles with 639: 578: 574: 569: 548: 543: 501: 491: 472: 461: 449: 421: 405: 400: 399: 376: 372: 345: 341: 334: 320: 316: 271:Phys. Rev. Lett 267: 263: 206: 202: 195: 181: 177: 170: 156: 152: 147: 123:polymer physics 104:Euclidean space 100:Minkowski space 85:renormalization 17: 12: 11: 5: 1805: 1795: 1794: 1789: 1784: 1779: 1774: 1758: 1757: 1750: 1743: 1735: 1732: 1731: 1714: 1697: 1696: 1694: 1693: 1680: 1672: 1669: 1668: 1666: 1665: 1660: 1655: 1650: 1649: 1648: 1637: 1635: 1631: 1630: 1628: 1627: 1621: 1619: 1615: 1614: 1612: 1611: 1604: 1599: 1594: 1589: 1583: 1581: 1577: 1576: 1574: 1573: 1568: 1563: 1558: 1553: 1548: 1543: 1537: 1535: 1529: 1528: 1525: 1524: 1522: 1521: 1516: 1511: 1506: 1501: 1496: 1491: 1486: 1481: 1475: 1473: 1464: 1463: 1462: 1461: 1456: 1446: 1445: 1444: 1439: 1429: 1424: 1423: 1422: 1412: 1411: 1410: 1405: 1400: 1395: 1390: 1385: 1380: 1370: 1369: 1368: 1363: 1352: 1350: 1342: 1341: 1339: 1338: 1333: 1328: 1319: 1308: 1306: 1300: 1299: 1297: 1296: 1291: 1290: 1289: 1284: 1279: 1274: 1264: 1263: 1262: 1257: 1252: 1247: 1237: 1236: 1235: 1230: 1225: 1220: 1210: 1209: 1208: 1198: 1197: 1196: 1191: 1181: 1180: 1179: 1177:Control theory 1174: 1164: 1163: 1162: 1157: 1152: 1142: 1141: 1140: 1135: 1130: 1120: 1119: 1118: 1108: 1102: 1100: 1094: 1093: 1091: 1090: 1085: 1080: 1075: 1070: 1064: 1062: 1056: 1055: 1052: 1051: 1049: 1048: 1043: 1038: 1033: 1028: 1023: 1018: 1013: 1008: 1002: 1000: 991: 990: 985: 980: 975: 970: 969: 968: 958: 953: 948: 943: 938: 937: 936: 931: 920: 918: 912: 911: 904: 903: 896: 889: 881: 872: 871: 869: 868: 867: 866: 861: 856: 849:Complex system 846: 841: 840: 839: 834: 823: 821: 817: 816: 814: 813: 808: 803: 798: 793: 787: 785: 779: 778: 776: 775: 774: 773: 768: 758: 752: 750: 744: 743: 741: 740: 731: 726: 721: 716: 711: 705: 703: 699: 698: 696: 695: 694: 693: 688: 677: 676: 675: 670: 665: 660: 649: 647: 641: 640: 638: 637: 632: 631: 630: 625: 620: 615: 604: 599: 594: 588: 586: 580: 579: 572: 570: 568: 567: 565:ergodic theory 562: 556: 554: 550: 549: 542: 541: 534: 527: 519: 513: 512: 507: 500: 499:External links 497: 496: 495: 489: 476: 470: 459: 453: 447: 432: 419: 404: 401: 398: 397: 370: 339: 332: 314: 261: 200: 193: 175: 169:978-0198539643 168: 149: 148: 146: 143: 15: 9: 6: 4: 3: 2: 1804: 1793: 1790: 1788: 1785: 1783: 1780: 1778: 1775: 1773: 1770: 1769: 1767: 1756: 1751: 1749: 1744: 1742: 1737: 1736: 1730: 1728: 1724: 1720: 1715: 1712: 1708: 1707: 1703: 1692: 1688: 1684: 1681: 1679: 1678: 1674: 1673: 1670: 1664: 1661: 1659: 1656: 1654: 1651: 1647: 1644: 1643: 1642: 1639: 1638: 1636: 1634:Organizations 1632: 1626: 1623: 1622: 1620: 1616: 1609: 1605: 1603: 1600: 1598: 1595: 1593: 1590: 1588: 1585: 1584: 1582: 1578: 1572: 1569: 1567: 1564: 1562: 1559: 1557: 1554: 1552: 1549: 1547: 1544: 1542: 1539: 1538: 1536: 1534: 1530: 1520: 1517: 1515: 1512: 1510: 1507: 1505: 1502: 1500: 1497: 1495: 1494:Quantum group 1492: 1490: 1487: 1485: 1482: 1480: 1477: 1476: 1474: 1472: 1468: 1460: 1457: 1455: 1452: 1451: 1450: 1449:Supersymmetry 1447: 1443: 1440: 1438: 1435: 1434: 1433: 1432:String theory 1430: 1428: 1425: 1421: 1418: 1417: 1416: 1413: 1409: 1406: 1404: 1401: 1399: 1396: 1394: 1391: 1389: 1386: 1384: 1381: 1379: 1376: 1375: 1374: 1371: 1367: 1364: 1362: 1359: 1358: 1357: 1354: 1353: 1351: 1349: 1343: 1337: 1334: 1332: 1331:Path integral 1329: 1327: 1323: 1320: 1317: 1313: 1312:Distributions 1310: 1309: 1307: 1305: 1301: 1295: 1292: 1288: 1285: 1283: 1280: 1278: 1275: 1273: 1270: 1269: 1268: 1265: 1261: 1258: 1256: 1253: 1251: 1248: 1246: 1243: 1242: 1241: 1238: 1234: 1231: 1229: 1226: 1224: 1221: 1219: 1216: 1215: 1214: 1211: 1207: 1204: 1203: 1202: 1199: 1195: 1192: 1190: 1187: 1186: 1185: 1182: 1178: 1175: 1173: 1170: 1169: 1168: 1165: 1161: 1158: 1156: 1153: 1151: 1148: 1147: 1146: 1143: 1139: 1136: 1134: 1131: 1129: 1126: 1125: 1124: 1121: 1117: 1114: 1113: 1112: 1109: 1107: 1104: 1103: 1101: 1099: 1095: 1089: 1086: 1084: 1081: 1079: 1078:Combinatorics 1076: 1074: 1071: 1069: 1066: 1065: 1063: 1061: 1057: 1047: 1044: 1042: 1039: 1037: 1034: 1032: 1029: 1027: 1024: 1022: 1019: 1017: 1014: 1012: 1009: 1007: 1004: 1003: 1001: 999: 995: 989: 986: 984: 981: 979: 976: 974: 971: 967: 964: 963: 962: 959: 957: 954: 952: 951:Coding theory 949: 947: 944: 942: 939: 935: 932: 930: 927: 926: 925: 922: 921: 919: 917: 916:Computational 913: 909: 902: 897: 895: 890: 888: 883: 882: 879: 865: 862: 860: 857: 855: 852: 851: 850: 847: 845: 842: 838: 837:superfluidity 835: 833: 830: 829: 828: 825: 824: 822: 818: 812: 809: 807: 804: 802: 799: 797: 794: 792: 789: 788: 786: 784: 780: 772: 769: 767: 764: 763: 762: 759: 757: 754: 753: 751: 749: 745: 739: 735: 732: 730: 727: 725: 722: 720: 717: 715: 712: 710: 707: 706: 704: 700: 692: 689: 687: 684: 683: 682: 678: 674: 671: 669: 666: 664: 661: 659: 656: 655: 654: 651: 650: 648: 646: 642: 636: 633: 629: 626: 624: 621: 619: 616: 614: 611: 610: 608: 605: 603: 600: 598: 595: 593: 590: 589: 587: 585: 581: 566: 563: 561: 558: 557: 555: 551: 547: 540: 535: 533: 528: 526: 521: 520: 517: 511: 508: 506: 503: 502: 492: 490:0-387-96477-0 486: 482: 477: 473: 471:0-691-08144-1 467: 463: 454: 450: 444: 440: 439: 433: 431: 430:0-521-40805-9 427: 422: 420:0-521-40806-7 416: 412: 407: 406: 393: 389: 385: 381: 374: 366: 362: 358: 354: 350: 343: 335: 329: 325: 318: 310: 306: 302: 298: 294: 290: 285: 280: 276: 272: 265: 257: 253: 249: 245: 241: 237: 233: 229: 224: 219: 215: 211: 204: 196: 190: 186: 179: 171: 165: 161: 154: 150: 142: 140: 136: 132: 128: 124: 119: 117: 113: 109: 105: 101: 97: 96:Wick rotation 92: 90: 86: 82: 78: 74: 70: 66: 62: 58: 54: 50: 46: 45:superfluidity 42: 38: 34: 30: 26: 22: 1727:expanding it 1716: 1701: 1689: / 1685: / 1675: 1551:Optimization 1514:Superalgebra 1402: 1373:Field theory 1346:Mathematical 1324: / 1172:Chaos theory 1155:Gauge theory 1083:Graph theory 978:Cryptography 826: 820:Applications 771:size scaling 480: 457: 437: 410: 383: 379: 373: 356: 352: 342: 323: 317: 274: 270: 264: 213: 210:Phys. Rev. E 209: 203: 184: 178: 159: 153: 120: 93: 28: 24: 18: 1691:topics list 1625:Mathematics 1541:Game theory 1442:Topological 1408:Topological 1403:Statistical 1366:Hamiltonian 811:von Neumann 681:force field 673:percolation 69:microstates 63:comprise a 1766:Categories 1597:Psychology 1561:Statistics 1361:Lagrangian 988:Statistics 924:Algorithms 668:Heisenberg 403:References 135:copolymers 129:, such as 127:biophysics 59:where the 1602:Sociology 1592:Chemistry 1388:Effective 1383:Conformal 1378:Classical 1250:Geometric 1223:Geometric 791:Boltzmann 714:H-theorem 592:Ensembles 309:119364261 37:magnetism 1677:Category 1326:analysis 1245:Exterior 1218:Exterior 1098:Analysis 1060:Discrete 934:analysis 801:Tsallis 458:The P(φ) 256:23431707 248:11970240 1687:outline 1618:Related 1587:Biology 1437:Bosonic 1398:Quantum 1348:physics 1314: ( 1046:Solvers 796:Shannon 783:Entropy 380:Polymer 353:Polymer 289:Bibcode 228:Bibcode 131:polymer 53:wetting 1260:Vector 1255:Tensor 1233:Vector 1228:Tensor 929:design 645:Models 553:Theory 487:  468:  445:  428:  417:  330:  307:  254:  246:  191:  166:  1717:This 1393:Gauge 854:chaos 806:RĂ©nyi 663:Potts 658:Ising 305:S2CID 279:arXiv 252:S2CID 218:arXiv 145:Notes 98:from 65:field 1723:stub 736:and 485:ISBN 466:ISBN 443:ISBN 426:ISBN 415:ISBN 328:ISBN 244:PMID 189:ISBN 164:ISBN 83:and 388:doi 361:doi 351:". 297:doi 236:doi 137:or 125:or 102:to 29:SFT 19:In 1768:: 609:: 384:48 382:. 357:47 355:. 303:. 295:. 287:. 275:83 273:. 250:. 242:. 234:. 226:. 214:60 212:. 141:. 118:. 91:. 51:, 47:, 43:, 39:, 23:, 1754:e 1747:t 1740:v 1729:. 1610:" 1606:" 1318:) 900:e 893:t 886:v 628:G 623:F 618:H 613:U 538:e 531:t 524:v 493:. 474:. 460:2 451:. 423:. 394:. 390:: 367:. 363:: 336:. 311:. 299:: 291:: 281:: 258:. 238:: 230:: 220:: 197:. 172:. 27:(

Index

theoretical physics
phase transitions
magnetism
superconductivity
superfluidity
topological phase transition
wetting
statistical mechanics
degrees of freedom
field
microstates
quantum field theory
quantum mechanics
path integral formulation
renormalization
polymer field theory
Wick rotation
Minkowski space
Euclidean space
correlation functions
Schwinger functions
Osterwalder–Schrader axioms
polymer physics
biophysics
polymer
copolymers
polyelectrolytes
ISBN
978-0198539643
ISBN

Text is available under the Creative Commons Attribution-ShareAlike License. Additional terms may apply.

↑