Perturbative renormalization group, exact results, and high-temperature series to order 21 for the N-vector spin models on the square lattice

Physical Review B - Condensed Matter and Materials Physics

Volumn 54, Issue 22, 1996, Pages 15828-15848

  Butera, P ^a   Comi, M ^a  

^a UNIVERSITY OF MILAN   (Italy)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0001692868     PISSN: 10980121     EISSN: 1550235X     Source Type: Journal    
DOI: 10.1103/PhysRevB.54.15828     Document Type: Article

References (98)

1. H. E. Stanley, Phys. Rev. Lett. 20, 589 (1968).
2. H. E. Stanley, Phys. Rev. 176, 718 (1968)
3. H. E. Stanley, Phys. Rev. 179, 570 (1969).
4. P. Butera and M. Comi, Phys. Rev. B 52, 6185 (1995).
5. P. Butera and M. Comi (unpublished).
6. F. Englert, Phys. Rev. 129, 567 (1963).
7. M. Wortis, in Phase Transitions and Critical Phenomena, edited by C. Domb and M. S. Green (Academic Press, London, 1974), Vol. 3.
8. S. McKenzie, in Phase Transitions Cargese 1980, edited by M. Levy, J. C. Le Guillou, and J. Zinn Justin (Plenum Press, New York 1982).
9. G. A. Baker and J. M. Kincaid, J. Stat. Phys. 24, 469 (1981).
10. G. A. Baker, Quantitative Theory of Critical Phenomena (Academic Press, Boston, 1990).
11. M. Luscher and P. Weisz, Nucl. Phys. B300, 325 (1988).
12. P. Butera, M. Comi and G. Marchesini, Nucl. Phys. B300, 1 (1988).
13. P. Butera, M. Comi and G. Marchesini, Phys. Rev. B 41, 11494 (1990).
14. R. P. Boas, Entire Functions (Academic Press, New York, 1954).
15. G. A. Baker and L. P. Benofy, J. Stat. Phys. 29, 699 (1982).
16. M. E. Fisher and K. Wilson, Phys. Rev. Lett. 28, 240 (1972).
17. R. B. Griffiths and P. D. Gujrati, J. Stat. Phys. 30, 563 (1983).
18. J. Cardy and H. Hamber, Phys. Rev. Lett. 45, 499 (1980).
19. B. Nienhuis, Phys. Rev. Lett. 49, 1062 (1982).
20. B. Nienhuis, J. Stat. Phys. 34, 731 (1984).
21. R. J. Baxter, J. Phys. A 19, 2821 (1986).
22. P. Butera and M. Comi, Phys. Rev. B 47, 11969 (1993).
23. P. Butera, M. Comi and G. Marchesini, Phys. Rev. B 40, 534 (1989).
24. P. Butera, M. Comi and G. Marchesini, Phys. Rev. B 33, 4725 (1986).
25. P. Butera, R. Cabassi, M. Comi and G. Marchesini, Comput. Phys. Comm. 44, 143 (1987).
26. P. Butera and M. Comi, Phys. Rev. B 50, 3052 (1994).
27. R. Kenna and A. C. Irving, Phys. Lett. B 351, 273 (1995); and (unpublished).
28. A. M. Polyakov, Phys. Lett. 59B, 79 (1975).
29. A. A. Migdal, JEPT 42, 743 (1976).
30. E. Brezin and J. Zinn-Justin, Phys. Rev. Lett. 36, 691 (1976).
31. E. Brezin and J. Zinn-Justin, Phys. Rev. B 14, 3110 (1976)
32. E. Brezin and J. Zinn-Justin, Phys. Rev. D 14, 2615 (1976)
33. W. A. Bardeen, B. W. Lee and R. E. Shrock, Phys. Rev. D 14, 985 (1976).
34. P. Butera, M. Comi, G. Marchesini and E. Onofri, Nucl. Phys. B326, 758 (1989).
35. A. Fernandez, J. Froelich, and A. Sokal, Random Walks, Critical Phenomena and Triviality in Quantum Field Theory (Springer-Verlag, Berlin, 1992).
36. H. E. Stanley, in Phase Transitions and Critical Phenomena, edited by C. Domb and M. S. Green (Academic Press, New York, 1974), Vol. 3.
37. D. MacDonald, D. L. Hunter, K. Kelly and N. Jan, J. Phys. A 25, 1429 (1992).
38. B. Masand, U. Wilenski, J. P. Maffar and S. Redner, J. Phys. A 25, L365 (1992).
39. A. R. Conway, I. G. Enting and A. J. Guttmann, J. Phys. A 26, 1519 (1993).
40. A. R. Conway and A. J. Guttmann (unpublished).
41. B. G. Nickel, in Phase Transitions: Cargese 1980, edited by M. Levy, J. C. Le Guillou, and J. Zinn-Justin (Plenum, New York, 1982).
42. S. Mckenzie, Can. J. Phys. 57, 1239 (1979).
43. M. Campostrini, A. Pelissetto, P. Rossi and E. Vicari, Nucl. Phys. B (Proc. Suppl.) 47, 755 (1995).
44. M. Campostrini, A. Pelissetto, P. Rossi and E. Vicari, Phys. Rev. D 54, 1782 (1996).
45. M. Campostrini, A. Pelissetto, P. Rossi and E. Vicari, Phys. Rev. B 54, 7301 (1996).
46. D. L. Hunter and G. A. Baker, Phys. Rev. B 7, 3346 (1973).
47. D. L. Hunter and G. A. Baker, Phys. Rev. B 7, 3377 (1973).
48. D. L. Hunter and G. A. Baker, Phys. Rev. B 19, 3808 (1979).
49. A. J. Guttmann, in Phase Transitions and Critical Phenomena, edited by C. Domb and J. Lebowitz (Academic Press, New York, 1989), Vol. 13.
50. A. J. Guttmann, J. Phys. A 20, 1839, (1987).
51. A. J. Guttmann, J. Phys. A 20, 1855 (1987).
52. M. E. Fisher and B. J. Hiley, J. Chem. Phys. 34, 1253 (1961).
53. E. Barouch, B. M. McCoy and T. T. Wu, Phys. Rev. Lett. 31, 1409 (1973).
54. A. Aharony and M. E. Fisher, Phys. Rev. Lett. 45, 679 (1980).
55. G. A. Baker, Phys. Rev. B 15, 1552 (1977).
56. B. Li, N. Madras and A. D. Sokal, J. Stat. Phys. 80, 661 (1995).
57. B. G. Nickel and B. Sharpe, J. Phys. A 12, 1819 (1979).
58. J. K. Kim, Phys. Lett. B 345, 469 (1995).
59. J. K. Kim and A. Patrascioiu, Phys. Rev. D 47, 2588 (1993).
60. J. Zinn-Justin, Quantum Field Theory and Critical Phenomena (Clarendon Press, Oxford, 1989).
61. M. Campostrini, A. Pelissetto, P. Rossi and E. Vicari, Nucl. Phys. B 459, 207 (1996).
62. J. C. Le Guillou and J. Zinn-Justin, Phys. Rev. B 21, 3976 (1980).
63. A. Patrascioiu and E. Seiler, Nucl. Phys. B (Proc. Suppl.) 30, 184 (1993).
64. G. E. Castilla and S. Chakravarty (unpublished).
65. M. Falcioni and A. Treves, Nucl. Phys. B265, 671 (1986).
66. S. Caracciolo and A. Pelissetto, Nucl. Phys. B455, 619 (1995).
67. R. G. Edwards, E. Ferreira, J. Goodman and A. D. Sokal, Nucl. Phys. B380, 621 (1992).
68. M. Luscher, P. Weisz and U. Wolff, Nucl. Phys. B359, 221 (1991).
69. S. Caracciolo, R. G. Edwards, A. Pelissetto and A. D. Sokal, Nucl. Phys. Proc. Suppl. B 47, 752 (1995).
70. S. Caracciolo, R. G. Edwards, A. Pelissetto and A. D. Sokal, Phys. Rev. Lett. 75, 1891 (1995) (unpublished).
71. S. Meyer (private communication) (to S. Caracciolo et al. quoted in Ref. 51).
72. P. Hasenfratz, M. Maggiore and F. Niedermayer, Phys. Lett. B 245, 522 (1990).
73. P. Hasenfratz and F. Niedermayer, Phys. Lett. B 245, 529 (1990).
74. F. W. J. Olver, Asymptotics and Special Functions (Academic Press, New York, 1974).
75. R. Brout, Physica A 177, 161 (1991).
76. R. Brout and W. Deans, Nucl. Phys. B215, 407 (1983).
77. J. L. Colot, J. Phys. A 16, 4423 (1983).
78. N. N. Khuri, Phys. Rev. D 12, 2298 (1975).
79. N. W. Dalton and D. W. Wood, Phys. Lett. 28A, 417 (1968).
80. G. Parisi, Phys. Lett. 90B, 111 (1980).
81. G. Martinelli, G. Parisi and R. Petronzio, Phys. Lett. 100B, 485 (1981).
82. T. Reisz, Nucl. Phys. B450, 569 (1995).
83. S. Caracciolo, R. G. Edwards, T. Mendes, A. Pelissetto and A. D. Sokal, Nucl. Phys. B (Proc. Suppl.) 47, 763 (1995).
84. B. Bonnier and M. Hontebeyrie, Phys. Lett. B226, 361 (1989); and in Rigorous Methods in Particle Physics, edited by S. Ciulli, F. Scheck, and W. Thirring (Springer, Berlin, 1990).
85. M. Falcioni, G. Martinelli, M. L. Paciello, B. Taglienti and G. Parisi, Nucl. Phys. B225, 313 (1983).
86. R. Basu and A. Guha, Phys. Rev. D 31, 1478 (1985).
87. D. S. Fisher and D. R. Nelson, Phys. Rev. B 16, 2300 (1977).
88. J. K. Kim, Phys. Rev. D 50, 4663 (1994).
89. U. Wolff, Phys. Lett. B 248, 335 (1990).
90. V. F. Muller, T. Raddatz and W. Ruhl, Nucl. Phys. B251, 212 (1985).
91. G. Cristofano, R. Musto, F. Nicodemi, R. Pettorino and F. Pezzella, Nucl. Phys. B257, 505 (1985).
92. J. M. Drouffe and H. Flyvbjerg, Phys. Lett. B 206, 285 (1988).
93. H. Flyvbjerg, Phys. Lett. B 219, 323 (1989).
94. H. Flyvbjerg and S. Varsted, Nucl. Phys. B344, 646 (1990).
95. P. Biscari, M. Campostrini and P. Rossi, Phys. Lett. B 242, 225 (1990).
96. M. Campostrini and P. Rossi, Phys. Lett. B 242, 81 (1990).
97. H. Flyvbjerg and F. Larsen, Phys. Lett. B 266, 92 (1991).
98. H. Flyvbjerg and F. Larsen, Phys. Lett. B 266, 99 (1991).