Universal amplitude ratios in the critical two-dimensional Ising model on a torus

Journal of Statistical Physics

Volumn 98, Issue 3-4, 2000, Pages 551-588

  Salas, Jesús ^a   Sokal, Alan D ^b  

^a UNIVERSITY OF ZARAGOZA   (Spain)

^b POLYTECHNIC UNIVERSITY   (United States)

Author keywords

Cluster algorithm; Conformal field theory; Corrections to scaling; Finite size scaling; Ising model; Monte Carlo; Swendsen Wang algorithm; Torus; Universal amplitude ratios

Indexed keywords

EID: 0034343056     PISSN: 00224715     EISSN: None     Source Type: Journal    
DOI: 10.1023/a:1018611122166     Document Type: Article

References (117)

1. C. Domb, The Critical Point: A Historical Introduction to the Modern Theory of Critical Phenomena (Taylor & Francis, London, 1996).
2. V. Privman, P. C. Hohenberg, and A. Aharony, in Phase Transitions and Critical Phenomena, Vol. 14, C. Domb and J. L. Lebowitz, eds. (Academic Press, London/San Diego, 1991).
3. B. Nienhuis, in Phase Transitions and Critical Phenomena, Vol. 11, C. Domb and J. L. Lebowitz, eds. (Academic Press, London, 1987).
4. J. L. Cardy, in Phase Transitions and Critical Phenomena, Vol. 11, C. Domb and J. L. Lebowitz, eds. (Academic Press, London, 1987).
5. C. Itzykson, H. Saleur, and J.-B. Zuber, eds., Conformal Invariance and Applications to Statistical Mechanics (World Scientific, Singapore, 1988).
6. P. Di Francesco, P. Mathieu and D. Sénéchal, Conformal Field Theory (Springer-Verlag, New York, 1997).
7. J. Zinn-Justin, Quantum Field Theory and Critical Phenomena, 2nd ed. (Clarendon Press, Oxford, 1993).
8. R. Guida and J. Zinn-Justin, J. Phys. A 31:8103 (1998), cond-mat/9803240.
9. G. Bhanot, M. Creutz, and J. Lacki, Phys. Rev. Lett. 69:1841 (1992), hep-lat/9206020.
10. J. Adler, C. Holm, and W. Janke, Physica A 201:581 (1993), hep-lat/9305005.
11. A. J. Guttmann and I. G. Enting, J. Phys. A 26:807 (1993), hep-lat/9212032.
12. A. J. Guttmann and I. G. Enting, J. Phys. A 27:5801 (1994), hep-lat/9312083.
13. H. Arisue and K. Tabata, Nucl. Phys. B 435:555 (1995), hep-lat/9407023.
14. P. Butera and M. Comi, Phys. Rev. E 55:6391 (1997), hep-lat/9703017.
15. P. Butera and M. Comi, Phys. Rev. B 56:8212 (1997), hep-lat/9703018.
16. P. Butera and M. Comi, Phys. Rev. B 60:6749 (1999), hep-lat/9903010.
17. C. Holm and W. Janke, Phys, Rev. B 48:936 (1993), hep-lat/9301002.
18. A. P. Gottlob and M. Hasenbusch, Physica A 201:593 (1993), cond-mat/9305020.
19. B. Li, N. Madras, and A. D. Sokal, J. Stat Phys. 80:661 (1995), hep-lat/9409003.
20. H. W. J. Blöte, E. Luitjen, and J. R. Heringa, J. Phys. A 28:6289 (1995), cond-mat/ 9509016.
21. M. P. Nightingale and H. W. J. Blöte, Phys. Rev. B 54:1001 (1996), cond-mat/9602089.
22. H. W. J. Blöte, J. R. Heringa, A. Hoogland, E. W. Meyer, and T. S. Smit, Phys. Rev. Lett. 76:2613 (1996), cond-mat/9602020.
23. S. Caracciolo, M. S. Causo, and A. Pelissetto, Phys. Rev. E 57:1215 (1998), cond-mat/ 9703250.
24. H. G. Ballesteros, L. A. Fernández, V. Martín-Mayor, and A. Muñoz Sudupe, Phys. Lett. B 441:330 (1998), cond-mat/9805022.
25. H. G. Ballesteros, L. A. Fernández, V. Martín-Mayor, A. Muñoz Sudupe, G. Parisi, and J. J. Ruiz-Lorenzo, J. Phys. A 32:1 (1999), cond-mat/9805125.
26. M. M. Tsypin and H. W. J. Blöte, Probability distribution of the order parameter for the 3D Ising model universality class: A high precision Monte Carlo study. Preprint, cond-mat/9909343.
27. S. Y. Zinn, S.-N. Lai, and M. E. Fisher, Phys. Rev. E 54:1176 (1996).
28. A. Pelissetto and E. Vicari, Nucl. Phys. B 519:626 (1998), cond-mat/9711078.
29. A. Pelissetto and E. Vicari, Nucl. Phys. B 522:605 (1998), cond-mat/9801098.
30. A. I. Sokolov and E. V. Orlov, Phys. Rev. B 58:2395 (1998), cond-mat/9804008.
31. J.-K. Kim, The critical renormalized coupling constants in the symmetric phase of the Ising models. Preprint, cond-mat/9905138.
32. S. Caracclolo, R. G. Edwards, A. Pelissetto, and A. D. Sokal, Phys. Rev. Lett. 75:1891 (1995). hep-lat/9411009.
33. S. Caracciolo, R. G. Edwards, T. Mendes, A. Pelissetto, and A. D. Sokal, Nucl. Phys. B (Proc. Suppl.) 47:763 (1996), hep-lat/9509033.
34. G. Mana, A. Pelissetto, and A. D. Sokal, Phys. Rev. D 55:3674 (1997), hep-lat/9610021.
35. J. Balog and M. Niedermaier, Nucl. Phys. B 500:421 (1997), hep-th/9612039.
36. J. Balog, M. Niedermaier, F. Niedermayer, A. Patrascioiu, E. Seiler, and P. Weisz, Phys. Rev. D 60:094508 (1999), hep-lat/9903036.
37. M. Caselle, R. Tateo, and S. Vinti, Universal amplitudes in the 2D four state Potts model. Preprint, cond-mat/9902146. Nucl. Phys. B, in press.
38. G. Delfino, G. T. Barkema, and J. Cardy, Susceptibility amplitude ratios in the two-dimensional Potts model and percolation. Preprint, cond-mat/9908453.
39. C. M. Naón, J. Phys. A 22:2877 (1989).
40. A. J. Liu and M. E. Fisher, Physica A 156:35 (1989).
41. J.-K. Kim and A. Patrascioiu, Phys. Rev. D 47:2588 (1993).
42. C. Gutsfeld, J. Küster, and G. Münster, Nucl. Phys. B 479:654 (1996), cond-mat/9606091.
43. S.-Y. Zinn and M. E. Fisher, Physica A 226:168 (1996).
44. R. Guida and J. Zinn-Justin, Nucl. Phys. B 489:626 (1997), hep-th/9610223.
45. M. Caselle and M. Hasenbusch, J. Phys. A 30:4963 (1997), hep-lat/9701007.
46. A. Pelissetto and E. Vicari, Nucl. Phys. B 540:639 (1999), cond-mat/9805317.
47. M. Weigel and W. Janke, Phys. Rev. Lett. 82:2318 (1999), cond-mat/9809253.
48. P. Butera and M. Comi, Phys. Rev. B 58:11552 (1998), hep-lat/9805025.
49. A. I. Sokolov, E. V. Orlov, V. A. Ul'kov, and S. S. Kashtanov, Phys. Rev. E 60:1344 (1999), hep-th/9810082.
50. A. C. Petkou and N. D. Vlachos, Phys. Lett. B 446:306 (1999), hep-th/9803146.
51. E. Luitjen, K. Binder, and H. W. J. Blöte, Eur: Phys. J. B 9:289 (1999), cond-mat/ 9901042.
52. T. T. Wu, B. M. McCoy, C. A. Tracy, and E. Barouch, Phys. Rev. B 13:316 (1976).
53. P. Di Francesco, H. Saleur, and J.-B. Zuber, Nucl. Phys. B 290[FS20]:527 (1987).
54. P. Di Francesco, H. Saleur, and J.-B. Zuber, Europhys. Lett. 5:95 (1988).
55. J. L. Cardy, Phys. Rev. Lett. 60:2709 (1988).
56. J. L. Cardy, J. Phys. A 21:L797 (1988).
57. J. L. Cardy and H. Saleur, J. Phys. A 22:L601 (1989).
58. S. Caracciolo, A. Pelissetto, and A. D. Sokal, J. Phys. A 23:L969 (1990).
59. J. L. Cardy and G. Mussardo, Nucl. Phys. B 410:451 (1993), hep-th/9306028.
60. J. L. Cardy and A. J. Guttmann, J. Phys. A 26:2485 (1993), cond-mat/9303035.
61. A. V. Smilga, Phys. Rev. D 55:R443 (1997), hep-th/9607154.
62. G. Delfino, Phys. Lett. B 419:291 (1998), hep-th/9710019.
63. G. Delfino and J. L. Cardy, Nucl. Phys. B 519:551 (1998), hep-th/9712111.
64. K. Binder, Z. Phys. B 43:119 (1981).
65. C. M. Newman, Z. Wahr. rerw. Geb. 33:75 (1975).
66. J. Bricmont, J. Stat. Phys. 17:289 (1977).
67. C. M. Newman, Commun. Math. Phys. 41:1 (1975).
68. S. B. Shlosman, Commun. Math. Phys. 102:679 (1986).
69. M. Lüscher, P. Weisz, and U. Wolff, Nucl. Phys. B 359:221 (1991).
70. J.-K. Kim, Phys. Rev. Lett. 70:1735 (1993).
71. S. Caracciolo, R. G. Edwards, S. J. Ferreira, A. Pelissetto, and A. D. Sokal, Phys. Rev. Lett. 74:2969 (1995), hep-lat/9409004.
72. S. Caracciolo, A. Pelissetto, and A.D. Sokal, in preparation.
73. V. Privman and M. E. Fisher, Phys. Rev. B 30:322 (1984).
74. J. L. Cardy, J. Phys. A 17:385 (1984).
75. J. Salas and A. D. Sokal, J. Stat. Phys. 87:1 (1997), hep-lat/9605018.
76. J. Salas and A. D. Sokal, J. Stat. Phys. 85:297 (1996), hep-lat/9511022.
77. J. Salas and A. D. Sokal, J. Stat. Phys. 88:567 (1997), hep-lat/9607030.
78. J. Salas and A. D. Sokal, J. Stat. Phys. 92:729 (1998), cond-mat/9801079.
79. S. J. Ferreira and A. D. Sokal, J. Stat. Phys. 96:461 (1999), cond-mat/9811345.
80. J.-K. Kim, private communication.
81. G. Kamieniarz and H. W. J. Blöte. J. Phys. A 26:201 (1993).
82. G. A. Baker Jr. and N. Kawashima, J. Phys. A 29:7183 (1996).
83. G. A. Baker Jr., J. Stat. Phys. 77:955 (1994).
84. P. Butera and N. Comi, Phys. Rev. B 54:15828 (1996), hep-lat/9710092.
85. J. C. LeGuillou and J. Zinn-Justin, Phys. Rev. B 21:3976 (1980).
86. C. M. Bender and S. Boettcher, Phys. Rev. D 48:4919 (1993), hep-th/9311060.
87. C. M. Bender and S. Boettcher, Phys. Rev. D 51:1875 (1995), hep-th/9405043.
88. R. H. Swendsen and J.-S. Wang, Phys. Rev. Lett. 58:86 (1987).
89. R. G. Edwards and A. D. Sokal, Phys. Rev. D 38:2009 (1988).
90. A. D. Sokal, in Functional Integration: Basics and Applications (1996 Cargèse summer school), C. DeWitt-Morette, P. Cartier, and A. Folacci, eds. (Plenum, New York, 1997).
91. P. W. Kasteleyn and C. M. Fortuin, J. Phys. Soc. Japan 26(Suppl.):11 (1969).
92. C. M. Fortuin and P. W. Kasteleyn, Physica 57:536 (1972).
93. C. M. Fortuin, Physica 58:393 (1972); 59:545 (1972).
94. C. M. Fortuin, Physica 58:393 (1972); 59:545 (1972).
95. N. Madras and A. D. Sokal, J. Stat. Phys. 50:109 (1988).
96. X.-J. Li and A. D. Sokal, Phys. Rev. Lett. 63:827 (1989).
97. H. G. Ballesteros, L. A. Fernández, V. Martín-Mayor, A. Muñoz Sudupe, G. Parisi, and J. J. Ruiz-Lorenzo, J. Phys. A 30:8379 (1998), cond-mat/9707179; and private communication.
98. U. Wolff, Phys. Rev. Lett. 62:3834 (1989).
99. V. Privman, in Finite Size Scaling and Numerical Simulation of Statistical Systems, V. Privman, ed. (World Scientific, Singapore, 1990).
100. H. Guo and D. Jasnow, Phys. Rev. B 35:1846 (1987); 39:753 (E) (1989).
101. H. Guo and D. Jasnow, Phys. Rev. B 35:1846 (1987); 39:753 (E) (1989).
102. A. Aharony and M. E. Fisher, Phys. Rev. B 27:4394 (1983).
103. S. Gartenhaus and W. S. McCullough, Phys. Rev. B 38:11688 (1988).
104. B. Nickel, J. Phys. A: Math. Gen. 32:3889 (1999).
105. B. Nickel, Addendum to "On the singularity structure of the 2-d Ising model susceptibility." University of Guelph preprint, June 1999.
106. A. Pelissetto, private communication (May 1999).
107. F. J. Wegner, Phys. Rev. B 5:4529 (1972).
108. F. J. Wegner, in Phase Transitions and Critical Phenomena, Vol. 6, C. Domb and M. S. Green, eds. (Academic Press, London, 1976).
109. J. Salas and A. D. Sokal, in preparation.
110. C. M. Newman, private communication (1999).
111. C. M. Newman, Commun. Math. Phys. 74:119 (1980).
112. C. M. Newman, Commun. Math. Phys. 91:75 (1983).
113. M. den Nijs, M. P. Nightingale, and M. Schick, Phys. Rev. B 26:2490 (1982).
114. J. K. Burton Jr. and C. L. Henley, J. Phys. A 30:8385 (1997), cond-mat/9708171.
115. S. Caracciolo, A. Pelissetto, J. Salas, and A. D. Sokal, work in progress.
116. C. Itzykson and J.-M. Drouffe. Statistical Field Theory (Cambridge University Press, Cambridge, 1989), Vol. 2.
117. I. S. Gradshteyn and I. M. Ryzhik, Table of Integrals, Series and Products (Academic Press, New York, 1965).