Fisher zeros of the Q-state Potts model in the complex temperature plane for nonzero external magnetic field

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

Volumn 58, Issue 6, 1998, Pages 7006-7012

  Kim, Seung Yeon ^a   Creswick, Richard J ^a  

^a UNIVERSITY OF SOUTH CAROLINA   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0000322401     PISSN: 1063651X     EISSN: None     Source Type: Journal    
DOI: 10.1103/PhysRevE.58.7006     Document Type: Article

References (70)

1. R. B. Potts, Proc. Cambridge Philos. Soc. 48, 106 (1952).
2. F. Y. Wu, Rev. Mod. Phys. 54, 235 (1982).
3. L. Onsager, Phys. Rev. 65, 117 (1944); PHRVAO
4. Phys. Rev.B. Kaufman, 76, 1232 (1949).
5. R. J. Baxter, J. Phys. C 6, L445 (1973).
6. M. P. M. den Nijs, J. Phys. A 12, 1857 (1979); JPHAC5
7. J. Phys. AB. Nienhuis, E. K. Riedel, and M. Schick, 13, L189 (1980)
8. R. B. Pearson, Phys. Rev. B 22, 2579 (1980); PRBMDO
9. Phys. Rev. BJ. Black and V. J. Emery, 23, 429 (1981);
10. Phys. Rev. BM. P. M. den Nijs, 27, 1674 (1983);
11. R. J. Creswick and S.-Y. Kim, J. Phys. A 30, 8785 (1997).
12. R. J. Baxter, J. Phys. A 15, 3329 (1982).
13. E. Buffernoir and S. Wallon, J. Phys. A 26, 3045 (1993).
14. C. N. Yang and T. D. Lee, Phys. Rev. 87, 404 (1952); PHRVAO
15. Phys. Rev.T. D. Lee and C. N. Yang, 87, 410 (1952).
16. R. Abe, Prog. Theor. Phys. 37, 1070 (1967); PTPKAV
17. Prog. Theor. Phys.R. Abe 38, 72 (1967);
18. Prog. Theor. Phys.M. Suzuki, 38, 1225 (1967);
19. Prog. Theor. Phys.M. Suzuki 38, 1243 (1967);
20. R. Kenna and C. B. Lang, Phys. Rev. E 49, 5012 (1994).
21. P. J. Kortman and R. B. Griffiths, Phys. Rev. Lett. 27, 1439 (1971).
22. M. E. Fisher, Phys. Rev. Lett. 40, 1610 (1978).
23. D. A. Kurtze and M. E. Fisher, Phys. Rev. B 20, 2785 (1979).
24. D. A. Kurtze and M. E. Fisher, J. Stat. Phys. 19, 205 (1978).
25. K. Uzelac, P. Pfeuty, and R. Jullien, Phys. Rev. Lett. 43, 805 (1979).
26. G. A. Baker, Jr., M. E. Fisher, and P. Moussa, Phys. Rev. Lett. 42, 615 (1979).
27. L. Mittag and M. J. Stephen, J. Stat. Phys. 35, 303 (1984);
28. Z. Glumac and K. Uzelac, J. Phys. A 27, 7709 (1994).
29. J. L. Cardy, Phys. Rev. Lett. 54, 1354 (1985).
30. M. E. Fisher, in Lectures in Theoretical Physics, edited by W. E. Brittin (University of Colorado Press, Boulder, 1965), Vol. 7c, p. 1.
31. S. Katsura, Prog. Theor. Phys. 38, 1415 (1967); PTPKAV
32. Prog. Theor. Phys.Y. Abe and S. Katsura, 43, 1402 (1970).
33. H. J. Brascamp and H. Kunz, J. Math. Phys. 15, 65 (1974).
34. P. P. Martin, Nucl. Phys. B 225, 497 (1983); NUPBBO
35. J. M. Maillard and R. Rammal, J. Phys. A 16, 353 (1983); JPHAC5
36. J. Phys. AP. P. Martin and R. Rammal, 19, L547 (1986);
37. J. Phys. AD. W. Wood, R. W. Turnbull, and J. K. Ball, 20, 3465 (1987);
38. J. C. A. d’Auriac, J. M. Maillard, G. Rollet, and F. Y. Wu, Physica A 206, 441 (1994).
39. G. Bhanot, J. Stat. Phys. 60, 55 (1990); JSTPBSN.
40. A. Alves, B. A. Berg, and R. Villanova, Phys. Rev. B 43, 5846 (1991).
41. P. P. Martin, in Integrable Systems in Statistical Mechanics, edited by G. M. D’Ariano, A. Montorsi, and M. G. Rasetti (World Scientific, Singapore, 1985), p. 129;
42. P. P. Martin, J. Phys. A 19, 3267 (1986); JPHAC5P.
43. P. Martin, Potts Models and Related Problems in Statistical Mechanics (World Scientific, Singapore, 1991);
44. C.-N. Chen, C.-K. Hu, and F. Y. Wu, Phys. Rev. Lett. 76, 169 (1996); PRLTAO
45. Phys. Rev. Lett.F. Y. Wu, G. Rollet, H. Y. Huang, J. M. Maillard, C.-K. Hu, and C.-N. Chen, 76, 173 (1996)
46. R. Kenna, Nucl. Phys. B, Proc. Suppl. 63, 646 (1998).
47. V. Matveev and R. Shrock, J. Phys. A 28, 1557 (1995); JPHAC5J.
48. Phys. AV. Matveev R. Shrock 29, 803 (1996).
49. V. Matveev and R. Shrock, Phys. Rev. E 54, 6174 (1996); PLEEE8
50. Phys. Rev. EH. Feldmann, R. Shrock, and S.-H. Tsai, 57, 1335 (1998);
51. H. Feldmann, A. J. Guttmann, I. Jensen, R. Shrock, and S.-H. Tsai, J. Phys. A 31, 2287 (1998).
52. C. Itzykson, R. B. Pearson, and J. B. Zuber, Nucl. Phys. B 220, 415 (1983).
53. V. Matveev and R. Shrock, J. Phys. A 28, 4859 (1995); JPHAC5
54. V. Matveev R. ShrockPhys. Rev. E 53, 254 (1996).
55. B. Stošic, S. Miloševic, and H. E. Stanley, Phys. Rev. B 41, 11 466 (1990); PRBMDOG.
56. Bhanot, M. Creutz, and J. Lacki, Phys. Rev. Lett. 69, 1841 (1992);PRLTAOG.
57. Bhanot, Nucl. Phys. B, Proc. Suppl. 30, 236 (1993); NPBSE7
58. G. Bhanot, M. Creutz, U. Glässner, I. Horvath, J. Lacki, K. Schilling, and J. Weckel, Phys. Rev. B 48, 6183 (1993); PRBMDOG.
59. Bhanot, M. Creutz, I. Horvath, J. Lacki, and J. Weckel, Phys. Rev. E 49, 2445 (1994); PLEEE8
60. Phys. Rev. ER. J. Creswick, 52, R5735 (1995).
61. R. J. Creswick and S.-Y. Kim, Phys. Rev. E 56, 2418 (1997).
62. R. J. Creswick and S.-Y. Kim, in Computer Simulation Studies in Condensed-Matter Physics, edited by D. P. Landau, K. K. Mon, and H.-B. Schüttler (Springer, Berlin, 1998), Vol. 10, p. 224.
63. S.-Y. Kim and R. J. Creswick, Phys. Rev. Lett. 81, 2000 (1998); PRLTAO
64. R. Bulirsch and J. Stoer, Numer. Math. 6, 413 (1964); NUMMA7
65. M. Henkel and G. Schütz, J. Phys. A 21, 2617 (1988).
66. R. J. Creswick, H. A. Farach, and C. P. Poole, Jr., Introduction to Renormalization Group Methods in Physics (John Wiley and Sons, New York, 1992).
67. I. G. Enting, J. Phys. A 7, 1617 (1974); JPHAC5
68. J. Phys. AI. G. Enting 10, 325 (1977).
69. A. J. Guttmann, in Phase Transitions and Critical Phenomena, edited by C. Domb and J. Lebowitz (Academic, New York, 1989), Vol. 13, p. 1.
70. I. G. Enting, J. Phys. A 7, 2181 (1974).