Two-point correlation function of three-dimensional [Formula Presented] models: The critical limit and anisotropy

Physical Review E - Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics

Volumn 57, Issue 1, 1998, Pages 184-210

  Campostrini, Massimo ^a   Pelissetto, Andrea ^a   Rossi, Paolo ^a   Vicari, Ettore ^a  

^a UNIVERSITY OF PISA   (Italy)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0000966320     PISSN: 1063651X     EISSN: None     Source Type: Journal    
DOI: 10.1103/PhysRevE.57.184     Document Type: Article

References (88)

1. M. E. Fisher and R. J. Burford, Phys. Rev. 156, 583 (1967)
2. J. Zinn-Justin, Quantum Field Theory and Critical Phenomena (Clarendon Press, Oxford, 1989), and references therein.
3. M. Campostrini, A. Pelissetto, P. Rossi, and E. Vicari, Europhys. Lett. 38, 577 (1997)
4. M. E. Fisher and A. Aharony, Phys. Rev. Lett. 31, 1238 (1973); PRLTAO
5. M. E. FisherA. AharonyPhys. Rev. B 7, 2818 (1974).
6. A. Aharony, Phys. Rev. B 7, 2834 (1974)
7. H. B. Tarko and M. E. Fisher, Phys. Rev. B 11, 1217 (1975)
8. S.-k. Ma, Phys. Rev. A 10, 1818 (1974)
9. S. Caracciolo, A. J. Guttmann, B. Li, A. Pelissetto, and A. D. Sokal (unpublished).
10. P. Rossi and Y. Brihaye, Physica A 126, 237 (1984)
11. A. Cucchieri, T. Mendes, A. Pelissetto, and A. D. Sokal, J. Stat. Phys. 86, 581 (1997)
12. The number pl depends on the dimensionality d of the space; more precisely it is a non-decreasing function of d. It can be obtained by pl=nl-nl-1 and the generating function ∑l=0∞nltl=∏m=1d1/(1-tm), which implies the asymptotic behavior nl→ld-1/d!(d-1)!.
13. T. T. Wu, B. M. McCoy, C. A. Tracy, and E. Barouch, Phys. Rev. B 13, 316 (1976)
14. G. S. Joyce, in Phase Transitions and Critical Phenomena, Vol. 2, edited by C. Domb and M. Green (Academic Press, New York, 1974).
15. K. Symanzik, in Mathematical Problems in Theoretical Physics, edited by R. Schrader et al., Lecture Notes in Physics Vol. 153 (Springer, Berlin, 1982);
16. Nucl. Phys. B 226, 187 (1983);
17. Nucl. Phys. B 226, 205 (1983).
18. R. Abe, Prog. Theor. Phys. 53, 1836 (1973); PTPKAV
19. Prog. Theor. Phys.R. Abe and S. Hikami, 54, 325 (1975).
20. G. Parisi, Cargèse Lectures (1973) (unpublished); J. Stat. Phys. 23, 49 (1980)
21. G. Parisi, Statistical Field Theory (Addison-Wesley, Reading, MA, 1988).
22. B. G. Nickel, J. Math. Phys. 19, 542 (1978)
23. A. Rajantie, Nucl. Phys. B 480, 729 (1996)
24. J. P. Eckmann, J. Magnen, and R. Sénéor, Commun. Math. Phys. 39, 251 (1975); CMPHAY
25. J. Magnen and R. Sénéor, Commun. Math. Phys. 56, 237 (1977); CMPHAY
26. J. S. Feldman and K. Osterwalder, Ann. Phys. (N.Y.) 97, 80 (1976).
27. E. Brezin, J. C. LeGuillou, and J. Zinn-Justin, Phys. Rev. D 15, 1544 (1977)
28. G. A. Baker, Jr., B. G. Nickel, M. S. Green, and D. I. Meiron, Phys. Rev. Lett. 36, 1351 (1977); PRLTAO
29. G. A. Baker, Jr., B. G. Nickel, and D. I. Meiron, Phys. Rev. B 17, 1365 (1978)
30. J. C. LeGuillou and J. Zinn-Justin, Phys. Rev. Lett. 39, 95 (1977); PRLTAO
31. J. C. LeGuillouJ. Zinn-JustinPhys. Rev. B 21, 3976 (1980).
32. B. G. Nickel, in Phase Transitions: Cargèse 1980, edited by M. Levy, J. C. Le Guillou, and J. Zinn-Justin (Plenum, New York, 1982);
33. Physica A 117, 189 (1991).
34. S. A. Antonenko and A. I. Sokolov, Phys. Rev. E 51, 1894 (1995).
35. M. Campostrini, A. Pelissetto, P. Rossi, and E. Vicari, Nucl. Phys. B 459, 207 (1996)
36. T. Reisz, Phys. Lett. B 360, 77 (1995)
37. G. A. Baker, Jr., Phys. Rev. B 15, 1552 (1976)
38. G. A. Baker, Jr. and J. M. Kincaid, Phys. Rev. Lett. 42, 1431 (1979); PRLTAO
39. G. A. Baker, Jr.J. M. KincaidJ. Stat. Phys. 24, 469 (1981).
40. S. Zinn, S.-N. Lai, and M. E. Fisher, Phys. Rev. E 54, 1176 (1996).
41. P. Butera and M. Comi, Phys. Rev. E 55, 6391 (1997).
42. J. K. Kim and A. Patrasciou, Phys. Rev. D 47, 2588 (1993)
43. M. M. Tsypin, Phys. Rev. Lett. 73, 2015 (1994)
44. G. A. Baker, Jr. and N. Kawashima, J. Phys. A 29, 7183 (1996).
45. J. K. Kim and D. P. Landau, in Proceedings of the Conference Lattice 96, St. Louis 1996, edited by C. Bernard, M. Golterman, M. Ogilvie, and J. Potvin [Nucl. Phys. B (Proc. Suppl.) 53, 706 (1997)].
46. J. C. Le Guillou and J. Zinn-Justin, Phys. Rev. B 21, 3976 (1980)
47. D. B. Murray and B. G. Nickel, University of Guelph report, 1991.
48. K. G. Wilson and M. E. Fisher, Phys. Rev. Lett. 28, 240 (1972)
49. M. Campostrini, A. Pelissetto, P. Rossi, and E. Vicari, Phys. Rev. B 54, 7301 (1996)
50. M. Campostrini, A. Pelissetto, P. Rossi, and E. Vicari, Phys. Lett. B 402, 141 (1997)
51. J. C. Le Guillou and J. Zinn-Justin, J. Phys. (France) Lett. 46, L137 (1985); JPSLBO
52. J. C. Le GuillouJ. Zinn-JustinJ. Phys. (France) 48, 19 (1987);
53. J. Phys. (France)J. C. Le GuillouJ. Zinn-Justin50, 1365 (1989).
54. S. Caracciolo, A. Cucchieri, T. Mendes, A. Pelissetto, P. Rossi, A. D. Sokal, and E. Vicari, Nucl. Phys. B (Proc. Suppl.) 47, 759 (1996).
55. P. Butera and M. Comi, Phys. Rev. B 52, 6185 (1995); PRBMDO
56. P. ButeraM. Phys. Rev. B Comi56, 8212 (1997).
57. A. J. Guttman, J. Phys. A 20, 1839 (1987).
58. A. J. Guttman, J. Phys. A 22, 2807 (1989).
59. D. MacDonald, D. L. Hunter, K. Kelly, and N. Jan, J. Phys. A 25, 1429 (1992).
60. On the cubic lattice the available series of u2, u3 and Mc2/MG2-1 are, respectively of the form β4∑i=09aiβi, β3∑i=09aiβi, and β6∑i=05aiβi, except for N=1 where they are of the form β6∑i=07aiβi, β5∑i=07aiβi, and β8∑i=03aiβi. These series can be derived from the strong-coupling expansion of G(x) presented in Appendix B. On the diamond lattice the available series of u2, u3 and Md2/MG2-1 are, respectively of the form β6∑i=013aiβi, β5∑i=013aiβi, and β6∑i=09aiβi; except for N=1 where they are of the form β8∑i=011aiβi, β7∑i=011aiβi, and β8∑i=07aiβi.
61. M. Ferer and M. Wortis, Phys. Rev. B 6, 3426 (1972)
62. For review on the resummation techniques see, for example, A. J. Guttmann, Phase Transitions and Critical Phenomena, edited by C. Domb and J. Lebowitz (Academic Press, New York, 1989), Vol. 13.
63. P. Grassberger, J. Phys. A 26, 2769 (1993).
64. H. W. J. Blöte, E. Luijten, and J. R. Heringa, J. Phys. A 28, 6289 (1995); JPHAC5
65. J. Phys. AG. A. Talapov and H. W. J. Blöte, 29, 5727 (1996).
66. A. Gottlob and M. Hasenbush, Physica A 201, 593 (1993)
67. K. Chen, A. M. Ferrenberg, and D. P. Landau, Phys. Rev. B 48, 3249 (1993); PRBMDO
68. C. Holm and W. Janke, Phys. Lett. A 173, 8 (1993); PYLAAG
69. C. HolmW. JankePhys. Rev. B 48, 936 (1993).
70. M. L. Glasser, Phys. Rev. B 25, 5996 (1982)
71. D. S. Ritchie and M. E. Fisher, Phys. Rev. B 5, 2688 (1972)
72. A. B. Zamolodchikov and Al. B. Zamolodchikov, Nucl. Phys. B 133, 525 (1978)
73. S. Caracciolo, G. Ferraro, and A. Pelissetto, J. Phys. A 24, 3625 (1991).
74. S. Caracciolo, M. S. Causo, and A. Pelissetto, J. Phys. A 30, 4939 (1997).
75. B. Li, N. Madras, and A. D. Sokal, J. Stat. Phys. 80, 661 (1995)
76. M. Caselle and M. Hasenbusch, J. Phys. A 30, 4963 (1997).
77. M. Campostrini, A. Pelissetto, P. Rossi, and E. Vicari, Phys. Rev. D 54, 1782 (1996)
78. D. L. Hunter and G. A. Baker, Jr., Phys. Rev. B 7, 3346, 3377 (1972); PLRBAQ
79. D. L. HunterG. A. Baker, Jr.Phys. Rev. B 19, 3808 (1979);
80. A. J. Guttmann and G. S. Joyce, J. Phys. A 5, L81 (1972); JPHAC5
81. J. Phys. AM. E. Fisher and H. Au-Yang, 12, 1677 (1979);
82. J. Phys. AM. E. FisherH. Au-Yang13, 1517 (1980).
83. M. Combescot, M. Droz, and J. M. Kosterlitz, Phys. Rev. B 11, 4661 (1974)
84. H. Arisue and K. Tabata, Nucl. Phys. B 435, 555 (1995)
85. On the cubic lattice the available series of r1 has the form β4∑i=09aiβi, except for N=1 where it has the form β6∑i=07aiβi. These series can be derived from the strong-coupling expansion of G(x) presented in Appendix B. On the diamond lattice the available series of r1 has the form β6∑i=013aiβi, except for N=1 where it has the form β8∑i=011aiβi.
86. H. Cheng and T. T. Wu, Phys. Rev. 164, 719 (1967)
87. E. Brezin, J. C. Le Guillou, and J. Zinn-Justin, Phys. Rev. D 8, 434 (1973)
88. I. S. Gradštein and I. M. Ryžik, Table of Integrals, Series and Products (Academic Press, Orlando, 1980).