Universality of the Ising and the S=1 model on Archimedean lattices: A Monte Carlo determination

Physical Review E - Statistical, Nonlinear, and Soft Matter Physics

Volumn 85, Issue 3, 2012, Pages

  Malakis, A ^a   Gulpinar, G ^b   Karaaslan, Y ^b   Papakonstantinou, T ^a   Aslan, G ^b  

^a UNIVERSITY OF ATHENS   (Greece)

^b DOKUZ EYLUL UNIVERSITY   (Turkey)

Author keywords

[No Author keywords available]

Indexed keywords

2D ISING MODEL; CRITICAL AMPLITUDES; CRITICAL EXPONENT; CRITICAL TEMPERATURES; FINITE SIZE ANALYSIS; FINITE-SIZE SCALING ANALYSIS; METROPOLIS ALGORITHMS; MONTE CARLO; MONTE CARLO DATA; MONTE CARLO SCHEMES; MONTE CARLO SIMULATION; PARALLEL TEMPERING;

ALGORITHMS; ISING MODEL;

MONTE CARLO METHODS;

EID: 84859407355     PISSN: 15393755     EISSN: 15502376     Source Type: Journal    
DOI: 10.1103/PhysRevE.85.031146     Document Type: Article

References (70)

1. M. E. Fisher, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.16.11 16, 11 (1966).
2. R. B. Griffiths, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett. 24.1479 24, 1479 (1970).
3. L. Onsager, Phys. Rev. PHRVAO 0031-899X 10.1103/PhysRev.65.117 65, 117 (1944).
4. B. Kaufman, Phys. Rev. PHRVAO 0031-899X 10.1103/PhysRev.76.1232 76, 1232 (1949).
5. C. N. Yang, Phys. Rev. PHRVAO 0031-899X 10.1103/PhysRev.85.808 85, 808 (1952).
6. R. J. Baxter, Exactly Solved Models in Statistical Mechanics (Academic Press, London, 1982).
7. J. C. Le Guillou, J. Zinn-Justin, Phys. Rev. B PRBMDO 1098-0121 10.1103/PhysRevB.21.3976 21, 3976 (1980).
8. A. M. Ferrenberg and D. P. Landau, Phys. Rev. B PRBMDO 1098-0121 10.1103/PhysRevB.44.5081 44, 5081 (1991).
9. H. W. J. Blote, E. Luijten, and J. R. Heringa, J. Phys. A JPHAC5 0305-4470 10.1088/0305-4470/28/22/007 28, 6289 (1995).
10. M. Hasenbusch, Phys. Rev. B PRBMDO 1098-0121 10.1103/PhysRevB.82.174433 82, 174433 (2010).
11. M. E. Fisher, in: Critical Phenomena, edited by, M. S. Green, (Academic Press, New York, 1971).
12. V. Privman (Ed.), Finite Size Scaling and Numerical Simulations of Statistical Systems (World Scientific, Singapore, 1990).
13. K. Binder, in: Computational Methods in Field Theory, edited by, H. Gausterer, and, C. B. Lang, (Springer, Berlin, 1992).
14. R. Kenna, D. A. Johnston, and W. Janke, Phys. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.96.115701 96, 115701 (2006);
15. R. Kenna, D. A. Johnston, and W. Janke, Phys. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.97.155702 97, 155702 (2006); (Pubitemid 44537106)
16. R. Kenna, D. A. Johnston, and W. Janke, Phys. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.97.169901 97, 169901 (E) (2006). (Pubitemid 44583234)
17. A. E. Ferdinand and M. E. Fisher, Phys. Rev. E PHRVAO 0031-899X 10.1103/PhysRev.185.832 185, 832 (1969).
18. A. Malakis, A. Peratzakis, and N. G. Fytas, Phys. Rev. E PLEEE8 1539-3755 10.1103/PhysRevE.70.066128 70, 066128 (2004). (Pubitemid 40429813)
19. N. Sh. Izmailian and C.-K. Hu, Phys. Rev. E PLEEE8 1539-3755 10.1103/PhysRevE.65.036103 65, 036103 (2002). (Pubitemid 40629641)
20. M.-C. Wu, C.-K. Hu, and N. Sh. Izmailian, Phys. Rev. E PLEEE8 1539-3755 10.1103/PhysRevE.67.065103 67, 065103 (2003).
21. J. Salas, J. Phys. A JPHAC5 0305-4470 10.1088/0305-4470/34/7/307 34, 1311 (2001).
22. L. N. Shchur and W. Janke, Nucl. Phys. B NUPBBO 0550-3213 10.1016/j.nuclphysb.2010.07.016 840, 491 (2010)
23. e-print arXiv: 1007.1838v1.
24. G. Kamieniarz and H. W. J. Blote, J. Phys. A: Math. Gen. JPHAC5 0305-4470 10.1088/0305-4470/26/2/009 26, 201 (1993).
25. W. Selke and L. N. Shchur, J. Phys. A: Math. Gen. JPHAC5 0305-4470 10.1088/0305-4470/38/44/L03 38, L739 (2005). (Pubitemid 41504021)
26. J. Salas and A. D. Sokal, J. Stat. Phys. JSTPBS 0022-4715 10.1023/A:1018611122166 98, 551 (1998).
27. F. W. S. Lima, J. Mostowicz, and K. Malarz, Commun. Comput. Phys. 10, 912 (2011).
28. R. Parviainen, Ph.D. Thesis, Uppsala University, Sweden, 2004.
29. P. N. Suding and R. M. Ziff, Phys. Rev. E PLEEE8 1539-3755 10.1103/PhysRevE.60.275 60, 275 (1999).
30. J. C. Wierman, Rand. Struct. Algs 1042-9832 10.1002/rsa.10029 20, 507 (2002). (Pubitemid 37340792)
31. C. R. Scullard and R. M. Ziff, Phys. Rev. E PLEEE8 1539-3755 10.1103/PhysRevE.73.045102 73, 045102 (R) (2006).
32. K. Malarz, M. Zborek, and B. Wróbel, TASK Quarterly 9, 475 (2005).
33. F. W. S. Lima and K. Malarz, Int. J. Mod. Phys. C IJMPEO 0129-1831 10.1142/S0129183106009849 17, 1273 (2006). (Pubitemid 44535028)
34. M. J. Krawczyk, K. Malarz, B. Kawecka-Magiera, A. Z. Maksymowicz, and K. Kulakowski, Phys. Rev. B PRBMDO 1098-0121 10.1103/PhysRevB.72.024445 72, 024445 (2005). (Pubitemid 43406437)
35. A. Codello, J. Phys. A: Math. Theor. 1751-8113 10.1088/1751-8113/43/38/ 385002 43, 385002 (2010).
36. J. B. Collins, P. A. Rikvold, and E. T. Gawlinski, Phys. Rev. B PRBMDO 1098-0121 10.1103/PhysRevB.38.6741 38, 6741 (1988).
37. M. Blume, Phys. Rev. PHRVAO 0031-899X 10.1103/PhysRev.141.517 141, 517 (1966).
38. H. W. Capel, Physica (Utr.) PHYSAG 0031-8914 10.1016/0031-8914(66)90027-9 32, 966 (1966);
39. H. W. Capel, Physica (Utr.) PHYSAG 0031-8914 10.1016/0031-8914(67)90167-X 33, 295 (1967);
40. H. W. Capel, Physica (Utr.) PHYSAG 0031-8914 10.1016/0031-8914(67)90198-X 37, 423 (1967).
41. M. Blume, V. J. Emery, and R. B. Griffiths, Phys. Rev. A PLRAAN 1050-2947 10.1103/PhysRevA.4.1071 4, 1071 (1971).
42. A. N. Berker and M. Wortis, Phys. Rev.B PRBMDO 1098-0121 10.1103/PhysRevB.14.4946 14, 4946 (1976).
43. D. P. Landau, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.28. 449 28, 449 (1972).
44. D. P. Landau and R. H. Swendsen, Phys. Rev. B PRBMDO 1098-0121 10.1103/PhysRevB.33.7700 33, 7700 (1986).
45. M. J. Stephen and J. L. McCauley Jr., Phys. Lett. A 0375-9601 10.1016/0375-9601(73)90799-8 44, 89 (1973);
46. T. S. Chang, G. F. Tuthill, and H. E. Stanley, Phys. Rev. B PRBMDO 1098-0121 10.1103/PhysRevB.9.4882 9, 4882 (1974);
47. G. F. Tuthill, J. F. Nicoll, and H. E. Stanley, Phys. Rev. B PRBMDO 1098-0121 10.1103/PhysRevB.11.4579 11, 4579 (1975);
48. F. J. Wegner, Phys. Lett. A PYLAAG 0375-9601 10.1016/0375-9601(75)90581-2 54, 1 (1975).
49. P. F. Fox and A. J. Guttmann, J. Phys. C JPSOAW 0022-3719 10.1088/0022-3719/6/5/020 6, 913 (1973);
50. T. W. Burkhardt and R. H. Swendsen, Phys. Rev. B PRBMDO 1098-0121 10.1103/PhysRevB.13.3071 13, 3071 (1976);
51. W. J. Camp and J. P. Van Dyke, Phys. Rev. B PRBMDO 1098-0121 10.1103/PhysRevB.11.2579 11, 2579 (1975);
52. D. M. Saul, M. Wortis, and D. Stauffer, Phys. Rev. B PRBMDO 1098-0121 10.1103/PhysRevB.9.4964 9, 4964 (1974).
53. P. Nightingale, J. Appl. Phys. JAPIAU 0021-8979 10.1063/1.330232 53, 7927 (1982). (Pubitemid 13491438)
54. P. D. Beale, Phys. Rev. B PRBMDO 1098-0121 10.1103/PhysRevB.33.1717 33, 1717 (1986).
55. A. Malakis, A. N. Berker, I. A. Hadjiagapiou, and N. G. Fytas, Phys. Rev. E PLEEE8 1539-3755 10.1103/PhysRevE.79.011125 79, 011125 (2009);
56. A. Malakis, A. N. Berker, I. A. Hadjiagapiou, N. G. Fytas, and T. Papakonstantinou, Phys. Rev. E PLEEE8 1539-3755 10.1103/PhysRevE.81.041113 81, 041113 (2010).
57. A. K. Jain and D. P. Landau, Phys. Rev. B PRBMDO 1098-0121 10.1103/PhysRevB.22.445 22, 445 (1980).
58. D. P. Landau and R. H. Swendsen, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.46.1437 46, 1437 (1981).
59. C. M. Care, J. Phys. A JPHAC5 0305-4470 10.1088/0305-4470/26/7/010 26, 1481 (1993).
60. M. Deserno, Phys. Rev. E PLEEE8 1539-3755 10.1103/PhysRevE.56.5204 56, 5204 (1997).
61. C. J. Silva, A. A. Caparica, and J. A. Plascak, Phys. Rev. E PLEEE8 1539-3755 10.1103/PhysRevE.73.036702 73, 036702 (2006). (Pubitemid 43352296)
62. R. H. Swendsen and J. S. Wang, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.58.86 58, 86 (1987);
63. U. Wolff, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.62.361 62, 361 (1989).
64. M. E. J Newman and G. T. Barkema, Monte Carlo Methods in Statistical Physics (Clarendon, Oxford, 1999).
65. D. P. Landau and K. Binder, Monte Carlo Simulations in Statistical Physics (Cambridge University Press, Cambridge, 2000).
66. Y. Deng and H. W. J. Blote, J. Phys. A: Math. Gen. JPHAC5 0305-4470 10.1088/0305-4470/28/22/007 28, 6289 (1995).
67. E. Bittner and W. Janke, Phys. Rev. E 1539-3755 10.1103/PhysRevE.84. 036701 84, 036701 (2011)
68. e-print arXiv: 1107.5640.
69. N. Metropolis, A. W. Rosenbluth, M. N. Rosenbluth, A. H. Teller, and E. Teller, J. Chem. Phys. JCPSA6 0021-9606 10.1063/1.1699114 21, 1087 (1953).
70. K. Binder, Z. Phys. B ZPCMDN 0722-3277 10.1007/BF01293604 43, 119 (1981).