The strength of first and second order phase transitions from partition function zeroes

Journal of Statistical Physics

Volumn 102, Issue 5-6, 2001, Pages 1211-1227

  Janke, W ^a   Kenna, R ^b  

^a UNIVERSITY OF LEIPZIG   (Germany)

^b TRINITY COLLEGE DUBLIN   (Ireland)

Author keywords

Critical exponents; Density of partition function zeroes; Finite size scaling; Latent heat; Phase transitions

Indexed keywords

EID: 0035534225     PISSN: 00224715     EISSN: None     Source Type: Journal    
DOI: 10.1023/A:1004836227767     Document Type: Article

References (95)

1. 1. K. Binder, in Computational Methods in Field Theory, Proceedings of the 31st Internationale Universitätswochen für Kern- and Teilchenphysik, Schladming, Austria, H. Gausterer and C. B. Lang, eds. (Springer-Verlag, Heidelberg, 1992). p. 59.
2. 2. W. Janke, in Computer Simulations in Condensed Matter Physics VII, D. P. Landau, K. K. Mon, and H.-B. Schüttler, eds. (Springer-Verlag, Heidelberg, Berlin, 1994). p. 29.
3. 3. A. Billoire, Nucl. Phys. B (Proc. Suppl.) 42:21 (1995).
4. 4. M. S. S. Challa, D. P. Landau, and K. Binder, Phys. Rev. B 34:1841 (1986).
5. 5. C. Borgs and J. Imbrie, Commun. Math. Phys. 123:305 (1989); C. Borgs and R. Kotecký, J. Stat. Phys. 61:79 (1990). C. Borgs, R. Kotecký, and R. H. Miracle-Sole, J. Stat. Phys. 62:529 (1991).
6. 5. C. Borgs and J. Imbrie, Commun. Math. Phys. 123:305 (1989); C. Borgs and R. Kotecký, J. Stat. Phys. 61:79 (1990). C. Borgs, R. Kotecký, and R. H. Miracle-Sole, J. Stat. Phys. 62:529 (1991).
7. 5. C. Borgs and J. Imbrie, Commun. Math. Phys. 123:305 (1989); C. Borgs and R. Kotecký, J. Stat. Phys. 61:79 (1990). C. Borgs, R. Kotecký, and R. H. Miracle-Sole, J. Stat. Phys. 62:529 (1991).
8. 6. J. Lee and J. M. Kosterlitz, Phys. Rev. Lett. 65:137 (1990); Phys. Rev. B 43:3265 (1991).
9. 6. J. Lee and J. M. Kosterlitz, Phys. Rev. Lett. 65:137 (1990); Phys. Rev. B 43:3265 (1991).
10. 7. C. Borgs and W. Janke, Phys. Rev. Lett. 68:1738 (1992).
11. 8. W. Janke, Phys. Rev. B 47:14757 (1993).
12. 9. M. E. Fisher, in Critical Phenomena, Proceedings of the Enrico Fermi International School of Physics. Vol. 51, M. S. Green, ed. (Academic Press, New York, 1971), p. 1.
13. 10. M. N. Barber, in Phase Transitions and Critical Phenomena. Vol. 8, C. Domb and J. L. Lebowitz eds. (Academic Press, New York, 1983). p. 1.
14. 11. V. Privman (ed.), Finite Size Scaling and Numerical Simulation of Statistical Systems (World Scientific, Singapore, 1990).
15. 12. C. N. Yang and T. D. Lee, Phys. Rev. 87:404 (1952): ibid. 410.
16. 12. C. N. Yang and T. D. Lee, Phys. Rev. 87:404 (1952): ibid. 410.
17. 13. M. E. Fisher, in Lectures in Theoretical Physics. Vol. VIIC. W. E. Brittin. ed. (Gordon and Breach, New York, 1968). p. 1.
18. 14. C. Itzykson, R. B. Pearson, and J. B. Zuber, Nucl. Phys. B 220:415 (1983).
19. 15. M. L. Glasser, V. Privman, and L. S. Schulman, Phys. Rev. B 35:1841 (1987).
20. 16. R. Kenna and C. B. Lang, Phys. Lett. B 264:396 (1991): Nucl. Phys. B 393:461 (1993): ibid. B 411:340 (1994) (Erratum).
21. 16. R. Kenna and C. B. Lang, Phys. Lett. B 264:396 (1991): Nucl. Phys. B 393:461 (1993): ibid. B 411:340 (1994) (Erratum).
22. 16. R. Kenna and C. B. Lang, Phys. Lett. B 264:396 (1991): Nucl. Phys. B 393:461 (1993): ibid. B 411:340 (1994) (Erratum).
23. 17. R. Kenna and C. B. Lang, Phys. Rev. E 49:5012 (1994).
24. 18. R. Kenna and A. C. Irving, Phys. Lett. B 351:273 (1995); Nucl. Phys. B 485:583 (1997): A. C. Irving and R. Kenna, Phys. Rev. B 53:11568 (1996).
25. 18. R. Kenna and A. C. Irving, Phys. Lett. B 351:273 (1995); Nucl. Phys. B 485:583 (1997): A. C. Irving and R. Kenna, Phys. Rev. B 53:11568 (1996).
26. 18. R. Kenna and A. C. Irving, Phys. Lett. B 351:273 (1995); Nucl. Phys. B 485:583 (1997): A. C. Irving and R. Kenna, Phys. Rev. B 53:11568 (1996).
27. 19. M. Suzuki and C. Kawabata, J. Phys. Soc. Japan 27:1105 (1969): C'. Kawabata and M. Suzuki, Phys. Lett. A 29:264 (1969): J. Phys. Soc. Japan 28:16 (1970): C. Kawabata, J. Phys. Soc. Japan 28:861 (1970): ibid. 1396: S. Katsura. Phys. Rev. 127:1508 (1962): ibid. 129:2835 (1963): Advances in Phys. 12:391 (1963).
28. 19. M. Suzuki and C. Kawabata, J. Phys. Soc. Japan 27:1105 (1969): C'. Kawabata and M. Suzuki, Phys. Lett. A 29:264 (1969): J. Phys. Soc. Japan 28:16 (1970): C. Kawabata, J. Phys. Soc. Japan 28:861 (1970): ibid. 1396: S. Katsura. Phys. Rev. 127:1508 (1962): ibid. 129:2835 (1963): Advances in Phys. 12:391 (1963).
29. 19. M. Suzuki and C. Kawabata, J. Phys. Soc. Japan 27:1105 (1969): C'. Kawabata and M. Suzuki, Phys. Lett. A 29:264 (1969): J. Phys. Soc. Japan 28:16 (1970): C. Kawabata, J. Phys. Soc. Japan 28:861 (1970): ibid. 1396: S. Katsura. Phys. Rev. 127:1508 (1962): ibid. 129:2835 (1963): Advances in Phys. 12:391 (1963).
30. 19. M. Suzuki and C. Kawabata, J. Phys. Soc. Japan 27:1105 (1969): C'. Kawabata and M. Suzuki, Phys. Lett. A 29:264 (1969): J. Phys. Soc. Japan 28:16 (1970): C. Kawabata, J. Phys. Soc. Japan 28:861 (1970): ibid. 1396: S. Katsura. Phys. Rev. 127:1508 (1962): ibid. 129:2835 (1963): Advances in Phys. 12:391 (1963).
31. 19. M. Suzuki and C. Kawabata, J. Phys. Soc. Japan 27:1105 (1969): C'. Kawabata and M. Suzuki, Phys. Lett. A 29:264 (1969): J. Phys. Soc. Japan 28:16 (1970): C. Kawabata, J. Phys. Soc. Japan 28:861 (1970): ibid. 1396: S. Katsura. Phys. Rev. 127:1508 (1962): ibid. 129:2835 (1963): Advances in Phys. 12:391 (1963).
32. 19. M. Suzuki and C. Kawabata, J. Phys. Soc. Japan 27:1105 (1969): C'. Kawabata and M. Suzuki, Phys. Lett. A 29:264 (1969): J. Phys. Soc. Japan 28:16 (1970): C. Kawabata, J. Phys. Soc. Japan 28:861 (1970): ibid. 1396: S. Katsura. Phys. Rev. 127:1508 (1962): ibid. 129:2835 (1963): Advances in Phys. 12:391 (1963).
33. 19. M. Suzuki and C. Kawabata, J. Phys. Soc. Japan 27:1105 (1969): C'. Kawabata and M. Suzuki, Phys. Lett. A 29:264 (1969): J. Phys. Soc. Japan 28:16 (1970): C. Kawabata, J. Phys. Soc. Japan 28:861 (1970): ibid. 1396: S. Katsura. Phys. Rev. 127:1508 (1962): ibid. 129:2835 (1963): Advances in Phys. 12:391 (1963).
34. 19. M. Suzuki and C. Kawabata, J. Phys. Soc. Japan 27:1105 (1969): C'. Kawabata and M. Suzuki, Phys. Lett. A 29:264 (1969): J. Phys. Soc. Japan 28:16 (1970): C. Kawabata, J. Phys. Soc. Japan 28:861 (1970): ibid. 1396: S. Katsura. Phys. Rev. 127:1508 (1962): ibid. 129:2835 (1963): Advances in Phys. 12:391 (1963).
35. 20. R. B. Pearson, Phys. Rev. B 26:6285 (1982).
36. 21. P. P. Martin, Nucl. Phys. B 220:366 (1983): ibid. 225:497 (1983).
37. 21. P. P. Martin, Nucl. Phys. B 220:366 (1983): ibid. 225:497 (1983).
38. 22. I. M. Harbour, A. J. Bell, M. Bernaschi, G. Salina, and A. Vladikas, Nucl. Phys. B 386:683 (1992); I. M. Barbour, R. Burioni. and G. Salina, Phys. Lett. B 341:355 (1995).
39. 22. I. M. Harbour, A. J. Bell, M. Bernaschi, G. Salina, and A. Vladikas, Nucl. Phys. B 386:683 (1992); I. M. Barbour, R. Burioni. and G. Salina, Phys. Lett. B 341:355 (1995).
40. 23. I. M. Barbour and E. G. Klepfish. Phys. Rev. B 46:469 (1992).
41. 24. I. M. Barbour, A. J. Bell, and E. G. Klepfish. Im. J. Mod. Phys. C 3:971 (1992): Nucl. Phys. B 389:285 (1993): I. M. Barbour and A. J. Bell, Nucl. Phys. B 372:385 (1992): I. M. Barbour, S. E. Morrison, E. G. Klepfish, J. B. Kogut, and M.-P. Lombardo. Phys. Rev. D 56:7063 (1997).
42. 24. I. M. Barbour, A. J. Bell, and E. G. Klepfish. Im. J. Mod. Phys. C 3:971 (1992): Nucl. Phys. B 389:285 (1993): I. M. Barbour and A. J. Bell, Nucl. Phys. B 372:385 (1992): I. M. Barbour, S. E. Morrison, E. G. Klepfish, J. B. Kogut, and M.-P. Lombardo. Phys. Rev. D 56:7063 (1997).
43. 24. I. M. Barbour, A. J. Bell, and E. G. Klepfish. Im. J. Mod. Phys. C 3:971 (1992): Nucl. Phys. B 389:285 (1993): I. M. Barbour and A. J. Bell, Nucl. Phys. B 372:385 (1992): I. M. Barbour, S. E. Morrison, E. G. Klepfish, J. B. Kogut, and M.-P. Lombardo. Phys. Rev. D 56:7063 (1997).
44. 24. I. M. Barbour, A. J. Bell, and E. G. Klepfish. Im. J. Mod. Phys. C 3:971 (1992): Nucl. Phys. B 389:285 (1993): I. M. Barbour and A. J. Bell, Nucl. Phys. B 372:385 (1992): I. M. Barbour, S. E. Morrison, E. G. Klepfish, J. B. Kogut, and M.-P. Lombardo. Phys. Rev. D 56:7063 (1997).
45. 25. S.-Y. Kim and R. J. Creswick, Phys. Rev. Lett. 81:2000 (1998); Phys. Rev. E 58:7006 (1998).
46. 25. S.-Y. Kim and R. J. Creswick, Phys. Rev. Lett. 81:2000 (1998); Phys. Rev. E 58:7006 (1998).
47. 26. V. Azcoiti, I. M. Barbour, R. Burioni, G. Di Carlo, A. F. Grillo, and G. Salina. Phys. Rev. D 51:5199 (1995).
48. 27. H. Gausterer and C. B. Lang, Phys. Lett. B 341:46 (1994): Nucl. Phys. B 455:785 (1995).
49. 27. H. Gausterer and C. B. Lang, Phys. Lett. B 341:46 (1994): Nucl. Phys. B 455:785 (1995).
50. 28. Ch. Hoelbling and C. B. Lang, Phys. Rev. B 54:3434 (1996).
51. 29. J. Jersák, C. B. Lang, and T. Neuhaus, Phys. Rev. Lett. 77:1933 (1996): Phys. Rev. D 54:6909 (1996); C. B. Lang and P. Petreczky, Phys. Lett. B 387:558 (1996).
52. 29. J. Jersák, C. B. Lang, and T. Neuhaus, Phys. Rev. Lett. 77:1933 (1996): Phys. Rev. D 54:6909 (1996); C. B. Lang and P. Petreczky, Phys. Lett. B 387:558 (1996).
53. 29. J. Jersák, C. B. Lang, and T. Neuhaus, Phys. Rev. Lett. 77:1933 (1996): Phys. Rev. D 54:6909 (1996); C. B. Lang and P. Petreczky, Phys. Lett. B 387:558 (1996).
54. 30. R. Villanova, Ph.D. Thesis (1991). Florida State University (unpublished).
55. 31. R. Villanova, N. A. Alves, and B. A. Berg. Nucl. Phys. B (Proc. Suppl.) 20:665 (1991): Phys. Rev. B 43:5846 (1991).
56. 31. R. Villanova, N. A. Alves, and B. A. Berg. Nucl. Phys. B (Proc. Suppl.) 20:665 (1991): Phys. Rev. B 43:5846 (1991).
57. 32. N. A. Alves, B. A. Berg, and R. Villanova. Phys. Rev. B 41:383 (1990).
58. 33. N. A. Alves. B. A. Berg, and S. Sanielevici. Phys. Rev. Lett. 64:3107 (1990): Nucl. Phys. B 376:218 (1992).
59. 33. N. A. Alves. B. A. Berg, and S. Sanielevici. Phys. Rev. Lett. 64:3107 (1990): Nucl. Phys. B 376:218 (1992).
60. 34. N. A. Alves, B. A. Berg. D. W. Duke. A. Irbäck, and S. Sanielevici, Phys. Lett. B 280:261 (1992).
61. 35. E. Marinari, Nucl. Phys. B 235:123 (1984).
62. 36. G. Bhanot, Nucl. Phys. B 343:467 (1990).
63. 37. G. Bhanot, S. Black, P. Carter, and R. Salvador, Phys. Lett. B 183:331 (1987): Phys. Rev. Lett. 59:803 (1987).
64. 37. G. Bhanot, S. Black, P. Carter, and R. Salvador, Phys. Lett. B 183:331 (1987): Phys. Rev. Lett. 59:803 (1987).
65. 38. M. Karliner, S. R. Sharpe, and Y. F. Chang, Nucl. Phys. B 302:204 (1988).
66. 39. E. Abraham, J. M. Barbour, P. H. Cullen, E. G. Klepfish. E. R. Pike, and S. Sarkar. Phys. Rev. B 53:7704 (1996).
67. 40. M. Suzuki, C. Kawabata, S. Ono, Y. Karaki, and M. Ikeda, J. Phys. Soc. Japan 29:837 (1970).
68. 41. H. Simon, M. Baake, and U. Grimm, in Proceedings of the 5th International Conference on Quasicrystals. C. Janot and R. Mosseri, eds. (World Scientific, Singapore, 1995). p. 100: Ch. Binck, Phys. Rev. Lett. 81:5644 (1998); R. J. Creswick and S.-Y. Kim, in Computer Simulation Studies in Condensed Matter Physics X, D. P. Landau, K. K. Mon, and H.-B. Schüttler, eds. (Springer, Berlin, 1998), p. 224; Comp. Phys. Comm. 121:26 (1999); R. Burioni, D. Cassi, and L. Donetti, J. Phys. A 32:5017 (1999).
69. 41. H. Simon, M. Baake, and U. Grimm, in Proceedings of the 5th International Conference on Quasicrystals. C. Janot and R. Mosseri, eds. (World Scientific, Singapore, 1995). p. 100: Ch. Binck, Phys. Rev. Lett. 81:5644 (1998); R. J. Creswick and S.-Y. Kim, in Computer Simulation Studies in Condensed Matter Physics X, D. P. Landau, K. K. Mon, and H.-B. Schüttler, eds. (Springer, Berlin, 1998), p. 224; Comp. Phys. Comm. 121:26 (1999); R. Burioni, D. Cassi, and L. Donetti, J. Phys. A 32:5017 (1999).
70. 41. H. Simon, M. Baake, and U. Grimm, in Proceedings of the 5th International Conference on Quasicrystals. C. Janot and R. Mosseri, eds. (World Scientific, Singapore, 1995). p. 100: Ch. Binck, Phys. Rev. Lett. 81:5644 (1998); R. J. Creswick and S.-Y. Kim, in Computer Simulation Studies in Condensed Matter Physics X, D. P. Landau, K. K. Mon, and H.-B. Schüttler, eds. (Springer, Berlin, 1998), p. 224; Comp. Phys. Comm. 121:26 (1999); R. Burioni, D. Cassi, and L. Donetti, J. Phys. A 32:5017 (1999).
71. 41. H. Simon, M. Baake, and U. Grimm, in Proceedings of the 5th International Conference on Quasicrystals. C. Janot and R. Mosseri, eds. (World Scientific, Singapore, 1995). p. 100: Ch. Binck, Phys. Rev. Lett. 81:5644 (1998); R. J. Creswick and S.-Y. Kim, in Computer Simulation Studies in Condensed Matter Physics X, D. P. Landau, K. K. Mon, and H.-B. Schüttler, eds. (Springer, Berlin, 1998), p. 224; Comp. Phys. Comm. 121:26 (1999); R. Burioni, D. Cassi, and L. Donetti, J. Phys. A 32:5017 (1999).
72. 41. H. Simon, M. Baake, and U. Grimm, in Proceedings of the 5th International Conference on Quasicrystals. C. Janot and R. Mosseri, eds. (World Scientific, Singapore, 1995). p. 100: Ch. Binck, Phys. Rev. Lett. 81:5644 (1998); R. J. Creswick and S.-Y. Kim, in Computer Simulation Studies in Condensed Matter Physics X, D. P. Landau, K. K. Mon, and H.-B. Schüttler, eds. (Springer, Berlin, 1998), p. 224; Comp. Phys. Comm. 121:26 (1999); R. Burioni, D. Cassi, and L. Donetti, J. Phys. A 32:5017 (1999).
73. 42. R. Abe, Prog. Theor. Phys. 37:1070 (1967); Prog. Theor. Phys. 38:72 (1967); ibid. 322: ibid. 568.
74. 42. R. Abe, Prog. Theor. Phys. 37:1070 (1967); Prog. Theor. Phys. 38:72 (1967); ibid. 322: ibid. 568.
75. 42. R. Abe, Prog. Theor. Phys. 37:1070 (1967); Prog. Theor. Phys. 38:72 (1967); ibid. 322: ibid. 568.
76. 42. R. Abe, Prog. Theor. Phys. 37:1070 (1967); Prog. Theor. Phys. 38:72 (1967); ibid. 322: ibid. 568.
77. 43. P. Butera, M. Comi, G. Marchesini, and E. Onofri, Nucl. Phys. B 326:758 (1989); P. H. Damgaard and U. M. Heller, Nucl. Phys. B 410:494 (1993); K.-C. Lee, Phys. Rev. Lett. 73:2801 (1994); V. Matveev and R. Shrock, Phys. Lett. A 204:353 (1995); M. Gürtler, E.-M. Ilgenfritz, and A. Schiller. Phys. Rev. D 56:3888 (1997).
78. 43. P. Butera, M. Comi, G. Marchesini, and E. Onofri, Nucl. Phys. B 326:758 (1989); P. H. Damgaard and U. M. Heller, Nucl. Phys. B 410:494 (1993); K.-C. Lee, Phys. Rev. Lett. 73:2801 (1994); V. Matveev and R. Shrock, Phys. Lett. A 204:353 (1995); M. Gürtler, E.-M. Ilgenfritz, and A. Schiller. Phys. Rev. D 56:3888 (1997).
79. 43. P. Butera, M. Comi, G. Marchesini, and E. Onofri, Nucl. Phys. B 326:758 (1989); P. H. Damgaard and U. M. Heller, Nucl. Phys. B 410:494 (1993); K.-C. Lee, Phys. Rev. Lett. 73:2801 (1994); V. Matveev and R. Shrock, Phys. Lett. A 204:353 (1995); M. Gürtler, E.-M. Ilgenfritz, and A. Schiller. Phys. Rev. D 56:3888 (1997).
80. 43. P. Butera, M. Comi, G. Marchesini, and E. Onofri, Nucl. Phys. B 326:758 (1989); P. H. Damgaard and U. M. Heller, Nucl. Phys. B 410:494 (1993); K.-C. Lee, Phys. Rev. Lett. 73:2801 (1994); V. Matveev and R. Shrock, Phys. Lett. A 204:353 (1995); M. Gürtler, E.-M. Ilgenfritz, and A. Schiller. Phys. Rev. D 56:3888 (1997).
81. 43. P. Butera, M. Comi, G. Marchesini, and E. Onofri, Nucl. Phys. B 326:758 (1989); P. H. Damgaard and U. M. Heller, Nucl. Phys. B 410:494 (1993); K.-C. Lee, Phys. Rev. Lett. 73:2801 (1994); V. Matveev and R. Shrock, Phys. Lett. A 204:353 (1995); M. Gürtler, E.-M. Ilgenfritz, and A. Schiller. Phys. Rev. D 56:3888 (1997).
82. 44. M. Suzuki, Prog. Theor. Phys. 38:289 (1967); ibid. 1225; ibid. 1243; Prog. Theor. Phys. 39:349 (1968).
83. 44. M. Suzuki, Prog. Theor. Phys. 38:289 (1967); ibid. 1225; ibid. 1243; Prog. Theor. Phys. 39:349 (1968).
84. 44. M. Suzuki, Prog. Theor. Phys. 38:289 (1967); ibid. 1225; ibid. 1243; Prog. Theor. Phys. 39:349 (1968).
85. 44. M. Suzuki, Prog. Theor. Phys. 38:289 (1967); ibid. 1225; ibid. 1243; Prog. Theor. Phys. 39:349 (1968).
86. 45. W. H. Press, B. P. Flannery, S. A. Teukolsky, and W. T. Vetterling, Numerical Recipes (Cambridge University Press, Cambridge, 1987). p. 503.
87. 46. R. J. Baxter. J. Phys. C 6:L445 (1973); J. Stat. Phys. 28:1 (1982).
88. 46. R. J. Baxter. J. Phys. C 6:L445 (1973); J. Stat. Phys. 28:1 (1982).
89. 47. F. Y. Wu, Rev. Mod. Phys. 54:235 (1982).
90. 48. W. Janke and R. Villanova, Nucl. Phys. B 489:679 (1997).
91. 49. N. A. Alves, J. R. Drugowich De Felicio, and U. H. E. Hansmann, J. Phys. A 33:7489 (2000).
92. 50. M. Weigel and W. Janke, Phys. Rev. B 62:6343 (2000).
93. 51. N. A. Alves, J. R. Drugowich De Felicio, and U. H. E. Hansmann, Int. J. Mod. Phys. C 8:1063 (1997).
94. 52. C. B. Lang, in Stochastic Analysis and Applications in Physics, Proc. of the NATO ASI in Funchal, Madeira, Aug. 1993, L. Streit, ed. (Kluwer Acad. Publishers, Dordrecht, 1994). p. 133.
95. 53. M. Baig and R. Villanova, Phys. Lett. B 333:445 (1994).