Dynamic critical behavior of the Swendsen - Wang algorithm for the three-dimensional Ising model

Nuclear Physics B

Volumn 691, Issue 3, 2004, Pages 259-291

  Ossola, Giovanni ^a   Sokal, Alan D ^a  

^a POLYTECHNIC UNIVERSITY   (United States)

Author keywords

Autocorrelation time; Cluster algorithm; Dynamic critical exponent; Ising model; Monte Carlo; Potts model; Swendsen Wang algorithm

Indexed keywords

EID: 3042608076     PISSN: 05503213     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.nuclphysb.2004.04.026     Document Type: Article

References (65)

1. Binder K. Monte Carlo Methods in Statistical Physics 1979 Springer-Verlag Berlin second ed., 1986
2. Binder K. Applications of the Monte Carlo Method in Statistical Physics 1984 Springer-Verlag Berlin second ed., 1987
3. Binder K. The Monte Carlo Method in Condensed Matter Physics 1992 Springer-Verlag Berlin second ed., 1995
4. Sokal A.D. Monte Carlo methods in statistical mechanics: foundations and new algorithms in: DeWitt-Morette C. Cartier P. Folacci A. (Eds.), Functional Integration: Basics and Applications, 1996 Cargèse Summer School 1997 131-192 Plenum New York
5. Newman M.E.J. Barkema G.T. Monte Carlo Methods in Statistical Physics 1999 Clarendon Oxford
6. Landau D.P. Binder K. A Guide to Monte Carlo Simulations in Statistical Physics 2000 Cambridge Univ. Press Cambridge
7. Binder K. Heermann D.W. Monte Carlo Simulation in Statistical Physics: An Introduction ed.
8. Janke W. Math. Comput. Simulation 47 1998 329
9. Swendsen R.H. Wang J.-S. Phys. Rev. Lett. 58 1987 86
10. Salas J. Sokal A.D. Universal amplitude ratios in the critical two-dimensional Ising model on a torus, cond-mat/9904038v1, see Section 6. For space reasons, this material was deleted from the published version of this paper J. Stat. Phys. 98 2000 551
11. Salas J. Sokal A.D. J. Stat. Phys. 87 1997 1, hep-lat/9605018
12. Salas J. Sokal A.D. J. Stat. Phys. 85 1996 297 hep-lat/9511022
13. Salas J. Sokal A.D. J. Stat. Phys. 88 1997 567 hep-lat/9607030
14. Wolff U. Phys. Lett. B 228 1989 379
15. Wang J.-S. Physica A 164 1990 240
16. Coddington P.D. Baillie C.F. Phys. Rev. Lett. 68 1992 962
17. Kerler W. Phys. Rev. D 47 1993 R1285
18. Kerler W. Phys. Rev. D 48 1993 902
19. Hennecke M. Heyken U. J. Stat. Phys. 72 1993 829
20. Wang J.-S. Kozan O. Swendsen R.H. Phys. Rev. E 66 2002 057101
21. Klein W. Ray T. Tamayo P. Phys. Rev. Lett. 62 1989 163
22. Ray T. Tamayo P. Klein W. Phys. Rev. A 39 1989 5949
23. Persky N. Ben-Av R. Kanter I. Domany E. Phys. Rev. E 54 1996 2351
24. M. Jerrum, T. Łuczak A.D. Sokal, E. Vigoda, The critical behavior for the Swendsen-Wang dynamics in the mean-field approximation, in preparation
25. Li X.-J. Sokal A.D. Phys. Rev. Lett. 63 1989 827
26. Wiseman S. Domany E. Phys. Rev. E 48 1993 4080
27. Ashkin J. Teller J. Phys. Rev. 64 1943 178
28. Baxter R.J. Exactly Solved Models in Statistical Mechanics 1982 Academic Press New York
29. Nienhuis B. J. Stat. Phys. 34 1984 731
30. Di Francesco P. Mathieu P. Sénéchal D. Conformal Field Theory 1997 Springer-Verlag New York
31. G. Ossola, A.D. Sokal, Critical exponents and universal amplitude ratios in the three-dimensional Ising universality class, in preparation
32. Edwards R.G. Sokal A.D. Phys. Rev. D 38 1988 2009
33. Kasteleyn P.W. Fortuin C.M. J. Phys. Soc. Jpn (Suppl.) 26 1969 11
34. Fortuin C.M. Kasteleyn P.W. Physica 57 1972 536
35. Fortuin C.M. Physica 59 1972 545
36. Anderson T.W. The Statistical Analysis of Time Series 1971 Wiley New York
37. Priestley M.B. Spectral Analysis and Time Series vols. 1, 2 1981 Academic Press London
38. Madras N. Sokal A.D. J. Stat. Phys. 50 1988 109
39. Blöte H.W.J. Shchur L.N. Talapov A.L. Int. J. Mod. Phys. C 10 1999 1137, cond-mat/9912005
40. Ballesteros H.G. Fernández L.A. Martín-Mayor V. Muñoz Sudupe A. Parisi G. Ruiz-Lorenzo J.J. J. Phys. A: Math. Gen. 32 1999 1, cond-mat/9805125
41. Hasenbusch M. Pinn K. Vinti S. Phys. Rev. B 59 1999 11471 hep-lat/9806012
42. Hasenbusch M. Int. J. Mod. Phys. C 12 2001 911
43. Knuth D.E. The Art of Computer Programming, vol. 2, 1981 Addison-Wesley Reading, MA
44. L'Ecuyer P. Math. Comp. 68 1999 249
45. Kalle C. Wansleben S. Comput. Phys. Commun. 33 1984 343
46. Filk T. Marcu M. Fredenhagen K. Phys. Lett. B 165 1985 125
47. Percus O.E. Percus J.K. J. Comput. Phys. 77 1988 267
48. G. Ossola, A.D. Sokal, Systematic errors due to linear congruential pseudo-random-number generators with the Swendsen-Wang algorithm, in preparation
49. See also Ossola G. Sokal A.D. hep-lat/0403010
50. Brézin E. Le Guillou J.C. Zinn-Justin J. Domb C. Green M.S. Phase Transitions and Critical Phenomena vol. 6 1976 Academic Press London
51. da Silva R. Alves N.A. Drugowich de Felício J.R. Phys. Lett. A 298 2002 325 cond-mat/0111288
52. Münkel C. Heermann D.W. Adler J. Gofman M. Stauffer D. Physica A 193 1993 540
53. Linke A. Heermann D.W. Altevogt P. Siegert M. Physica A 222 1995 205 cond-mat/9509115
54. Stauffer D. Physica A 244 1997 344
55. Li Z.B. Liu X.W. Schülke L. Zheng B. Physica A 245 1997 485 cond-mat/9705234
56. Ying H.-P. Wang L. Zhang J.-B. Jiang M. Hu J. Physica A 294 2001 111 cond-mat/0102500
57. Wansleben S. Landau D.P. Phys. Rev. B 43 1991 6006
58. Heuer H.-O. J. Phys. A: Math. Gen. 25 1992 L567
59. Grassberger P. Physica A 214 1995 547
60. Zheng B. Int. J. Mod. Phys. B 12 1998 1419
61. Jaster A. Mainville J. Schülke L. Zheng B. J. Phys. A: Math. Gen. 32 1999 1395 cond-mat/9808131
62. Ito N. Hukushima K. Ogawa K. Ozeki Y. J. Phys. Soc. Jpn. 69 2000 1931
63. Calabrese P. Martín-Mayor V. Pelissetto A. Vicari E. Phys. Rev. E 68 2003 016110 cond-mat/0301588
64. Hohenberg P.C. Halperin B.I. Rev. Mod. Phys. 49 1977 435
65. Heerman D.W. Burkitt A.N. Physica A 162 (1990) 210