Finite-size scaling of the density of zeros of the partition function in first- and second-order phase transitions

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

Volumn 56, Issue 3, 1997, Pages 2418-2422

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

^a UNIVERSITY OF SOUTH CAROLINA   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0000851927     PISSN: 1063651X     EISSN: None     Source Type: Journal    
DOI: 10.1103/PhysRevE.56.2418     Document Type: Article

References (69)

1. C N. Yang and T D. Lee, Phys. Rev.87, 404 (1952)
2. 87, 410 (1952).
3. M E. Fisher, in Lecture Notes in Theoretical Physics, edited by W. E. Brittin (University of Colorado Press, Boulder, 1965), Vol. 7c, p. 1.
4. R B. Griffiths, J. Math. Phys. (N.Y.)10, 1559 (1969).JMAPAQ
5. M. Suzuki and M E. Fisher, J. Math. Phys. (N.Y.)12, 235 (1971).JMAPAQ
6. R B. Pearson, Phys. Rev. B26, 6285 (1982).PRBMDO
7. C. Itzykson, R B. Pearson, and J B. Zuber, Nucl. Phys. B220, 415 (1983)
8. G. Bhanot, R. Salvador, S. Black, P. Carter, and R. Toral, Phys. Rev. Lett.59, 803 (1987).PRLTAO
9. F. Dunlop and C M. Newman, Commun. Math. Phys.44, 223 (1975).CMPHAY
10. B. Simon and R B. Griffiths, Commun. Math. Phys.33, 145 (1973)
11. C M. Newman, Commun. Pure Appl. Math.27, 143 (1974)
12. J. Stat. Phys.15, 399 (1976).JSTPBS
13. S. Katsura, Y. Abe, and K. Ohkouchi, J. Phys. Soc. Jpn.29, 845 (1970)
14. K S. Chang, S.-Y. Wang, and F Y. Wu, Phys. Rev. A4, 2324 (1971).PLRAAN
15. P P. Martin, Potts Models and Related Problems in Statistical Mechanics (World Scientific, Singapore, 1991), and references therein.
16. C.-N. Chen, C.-K. Hu, and F Y. Wu, Phys. Rev. Lett.76, 169 (1996), and references therein.PRLTAO
17. K.-C. Lee, Phys. Rev. Lett.73, 2801 (1994).PRLTAO
18. B. Derrida, L. De Seze, and C. Itzykson, J. Stat. Phys.33, 559 (1983).JSTPBS
19. R B. Griffiths, in Phase Transitions and Critical Phenomena, edited by C. Domb and M. S. Green (Academic, New York, 1973), Vol. 1, p. 8.
20. Finite Size Scaling and Numerical Simulation of Statistical Systems, edited by V. Privman (World Scientific, Singapore, 1990).
21. N N. Barber, in Phase Transitions and Critical Phenomena, edited by C. Domb and J. L. Lebowitz (Academic, New York, 1983), Vol. 8, p. 145.
22. D P. Landau, in Finite Size Scaling and Numerical Simulation of Statistical Systems (Ref. 15), and references
23. K. Binder, Rep. Prog. Phys.50, 783 (1987), and references therein.RPPHAG
24. Y. Imry, Phys. Rev. B21, 2042 (1980)
25. M E. Fisher and A N. Berker, 26, 2507 (1982)
26. J L. Cardy and M P. Nightingale, 27, 4256 (1983).
27. K. Binder and D P. Landau, Phys. Rev. B30, 1477 (1984)
28. M. S. S. Challa, D P. Landau, and K. Binder, 34, 1841 (1986).
29. J. Lee and J M. Kosterlitz, Phys. Rev. Lett.65, 137 (1990)
30. Phys. Rev. B43, 3265 (1991).PRBMDO
31. C. Borgs and R. Kotecký, J. Stat. Phys.61, 79 (1990)
32. Phys. Rev. Lett.68, 1734 (1992)
33. J. Stat. Phys.79, 43 (1995)
34. C. Borgs, R. Kotecký, and S. Miracle-Solé, 62, 529 (1991)
35. C. Borgs and W. Janke, Phys. Rev. Lett.68, 1738 (1992)
36. C. Borgs and J L. Imbrie, J. Stat. Phys.69, 487 (1992).JSTPBS
37. F Y. Wu, Rev. Mod. Phys.54, 235 (1982), and references therein.RMPHAT
38. P. Peczak and D P. Landau, Phys. Rev. B39, 11 932 (1989).PRBMDO
39. J F. McCarthy, Phys. Rev. B41, 9530 (1990).PRBMDO
40. R J. Baxter, J. Phys. C6, L445 (1973).JPSOAW
41. E. Buffenoir and S. Wallon, J. Phys. A26, 3045 (1993).JPHAC5
42. K M. Briggs, I G. Enting, and A J. Guttmann, J. Phys. A27, 1503 (1994); JPHAC5
43. A J. Guttmann and I G. Enting, 27, 5801 (1994).
44. G V. Bhanot, in Finite Size Scaling and Numerical Simulation of Statistical Systems (Ref. 15), and references
45. in Lattice 94, edited by F. Karsch, J. Engels, E. Laermann, and B. Petersson, special issue of Nucl. Phys. B, Proc. Suppl. 42 (1995).
46. The Early Universe, edited by E. W. Kolb and M. S. Turner (Addison-Wesley, Reading, MA, 1988)
47. M. Gleiser, Phys. Rev. Lett.73, 3495 (1994).PRLTAO
48. G. Bhanot, J. Stat. Phys.60, 55 (1990).JSTPBS
49. R J. Creswick, Phys. Rev. E52, R5735 (1995).PLEEE8
50. R. J. Creswick and S.-Y. Kim (unpublished).
51. R. Abe, Prog. Theor. Phys.38, 72 (1967)
52. M. Suzuki, 38, 1225 (1967).
53. P J. Kortman and R B. Griffiths, Phys. Rev. Lett.27, 1439 (1971).PRLTAO
54. M E. Fisher, Phys. Rev. Lett.40, 1610 (1978).PRLTAO
55. R. Bulirsch and J. Stoer, Numer. Math.6, 413 (1964); NUMMA7
56. M. Henkel and G. Schütz, J. Phys. A21, 2617 (1988).JPHAC5
57. M. Suzuki, C. Kawabata, S. Ono, Y. Karaki, and M. Ikeda, J. Phys. Soc. Jpn.29, 837 (1970).JUPSAU
58. C N. Yang, Phys. Rev.85, 808 (1952).PHRVAO
59. P D. Beale, Phys. Rev. Lett.76, 78 (1996).PRLTAO
60. R J. Creswick and A. Pavel’yev (unpublished).
61. R. J. Creswick and S.-Y. Kim (unpublished).
62. G. A. Baker, Jr., M E. Fisher, and P. Moussa, Phys. Rev. Lett.42, 615 (1979).PRLTAO
63. D A. Kurtze and M E. Fisher, J. Stat. Phys.19, 205 (1978)
64. Phys. Rev. B20, 2785 (1979)
65. K. Uzelac, P. Pfeuty, and R. Jullien, Phys. Rev. Lett.43, 805 (1979)
66. L. Mittag and M J. Stephen, J. Stat. Phys.35, 303 (1984)
67. Z. Glumac and K. Uzelac, J. Phys. A27, 7709 (1994).JPHAC5
68. J L. Cardy, Phys. Rev. Lett.54, 1354 (1985).PRLTAO
69. S.-Y. Kim and R. J. Creswick (unpublished).