Three-dimensional randomly dilute ising model: Monte Carlo results

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

Volumn 68, Issue 3 2, 2003, Pages 361361-361367

  Calabrese, Pasquale ^a   Martín Mayor, Victor ^b,c   Pelissetto, Andrea ^d   Vicari, Ettore ^e  

^a INFN SEZIONE DI PISA   (Italy)

^b UNIVERSIDAD COMPLUTENSE DE MADRID   (Spain)

^c UNIVERSITY OF ZARAGOZA   (Spain)

^d UNIVERSITÀ DI ROMA LA SAPIENZA   (Italy)

^e UNIVERSITY OF PISA   (Italy)

Author keywords

[No Author keywords available]

Indexed keywords

COMPUTER SIMULATION; FREE ENERGY; HAMILTONIANS; MAGNETIZATION; MONTE CARLO METHODS; PERTURBATION TECHNIQUES; RANDOM PROCESSES;

RANDOM DILUTE ISING MODEL (RIM); RENORMALIZATION GROUP (RG);

PHASE TRANSITIONS;

EID: 0242664679     PISSN: 1063651X     EISSN: None     Source Type: Journal    
DOI: None     Document Type: Article

References (76)

1. D.P. Belanger, Braz. J. Phys. 30, 682 (2000).
2. M. Campostrini, A. Pelissetto, P. Rossi, and E. Vicari, Phys. Rev. E 65, 066127 (2002); 60, 3526 (1999).
3. M. Campostrini, A. Pelissetto, P. Rossi, and E. Vicari, Phys. Rev. E 65, 066127 (2002); 60, 3526 (1999).
4. S. Fishman and A. Aharony, J. Phys. C 12, L729 (1979).
5. J.L. Cardy, Phys. Rev. B 29, 505 (1984).
6. D.P. Belanger, in Spin Glasses and Random Fields, edited by A.P. Young (World Scientific, Singapore, 1998), p. 251.
7. 2 [I.B. Ferreira, A.R, King, and V. Jaccarino, Phys. Rev. B 43, 10797 (1991)]. The theoretical estimate [P. Calabrese, A. Pelissetto, and E. Vicari, Phys. Rev. B (to be published), e-print cond-mat/0305041] φ= 1.42(2) is in good agreement.
8. 2 [I.B. Ferreira, A.R, King, and V. Jaccarino, Phys. Rev. B 43, 10797 (1991)]. The theoretical estimate [P. Calabrese, A. Pelissetto, and E. Vicari, Phys. Rev. B (to be published), e-print cond-mat/0305041] φ= 1.42(2) is in good agreement.
9. A. Aharony, in Phase Transitions and Critical Phenomena, edited by C. Domb and M.S. Green (Academic Press, New York, 1976), Vol. 6, p. 357.
10. R.B. Stinchcombe, in Phase Transitions and Critical Phenomena, edited by C. Domb and M.S. Green (Academic Press, New York, 1983), Vol. 7, p. 152.
11. A. Pelissetto and E. Vicari, Phys. Rep. 368, 549 (2002).
12. R. Folk, Yu. Holovatch, and T. Yavors'kii, Uspekhi Fiz. Nauk 173, 175 (2003) [Phys. Usp. 46, 175 (2003)].
13. R. Folk, Yu. Holovatch, and T. Yavors'kii, Uspekhi Fiz. Nauk 173, 175 (2003) [Phys. Usp. 46, 175 (2003)].
14. W. Selke, L.N. Shchur, and A.L. Talapov, in Annual Reviews of Computational Physics, Vol. I, edited by D. Stauffer (World Scientific, Singapore, 1995).
15. S. Wiseman and E. Domany, Phys. Rev. Lett. 81, 22 (1998); Phys. Rev. E 58, 2938 (1998).
16. S. Wiseman and E. Domany, Phys. Rev. Lett. 81, 22 (1998); Phys. Rev. E 58, 2938 (1998).
17. H.G. Ballesteros, L.A. Fernández, V. Martiń-Mayor, A. Mu noz Sudupe, G. Parisi, and J.J, Ruiz-Lorenzo, Phys. Rev. B 58, 2740 (1998).
18. K. Hukushima, J. Phys. Soc. Jpn. 69, 631 (2000).
19. M.I. Marqués, J.A. Gonzalo, and J. Iñiguez, Phys. Rev. E 62, 191 (2000).
20. W.C. Barber and D.P. Belanger, J. Magn. Magn. Mater. 226-230, 545 (2001).
21. P.E. Berche, C. Chatelain, B. Berche, and W. Janke, Comput. Phys. Commun. 147, 427 (2002).
22. G. Grinstein and A. Luther, Phys. Rev. B 13, 1329 (1976).
23. V.S. Dotsenko, B. Harris, D. Sherrington, and R. Stinchcombe, J. Phys. A 28, 3093 (1995); V.S. Dotsenko and D.E. Feldman, ibid. 28, 5183 (1995); V.S. Dotsenko, ibid. 32, 2949 (1999).
24. V.S. Dotsenko, B. Harris, D. Sherrington, and R. Stinchcombe, J. Phys. A 28, 3093 (1995); V.S. Dotsenko and D.E. Feldman, ibid. 28, 5183 (1995); V.S. Dotsenko, ibid. 32, 2949 (1999).
25. V.S. Dotsenko, B. Harris, D. Sherrington, and R. Stinchcombe, J. Phys. A 28, 3093 (1995); V.S. Dotsenko and D.E. Feldman, ibid. 28, 5183 (1995); V.S. Dotsenko, ibid. 32, 2949 (1999).
26. V.V. Prudnikov, P.V. Prudnikov, and A.A. Fedorenko, Phys. Rev. B 63, 184201 (2001); J. Phys. A 34, L145 (2001); A.A. Fedorenko, ibid. 36, 1239 (2003).
27. V.V. Prudnikov, P.V. Prudnikov, and A.A. Fedorenko, Phys. Rev. B 63, 184201 (2001); J. Phys. A 34, L145 (2001); A.A. Fedorenko, ibid. 36, 1239 (2003).
28. V.V. Prudnikov, P.V. Prudnikov, and A.A. Fedorenko, Phys. Rev. B 63, 184201 (2001); J. Phys. A 34, L145 (2001); A.A. Fedorenko, ibid. 36, 1239 (2003).
29. A.J. Bray, T. McCarthy, M.A. Moore, J.D. Reger, and A.P. Young, Phys. Rev. B 36, 2212 (1987); A.J. McKane, ibid. 49, 12003 (1994).
30. A.J. Bray, T. McCarthy, M.A. Moore, J.D. Reger, and A.P. Young, Phys. Rev. B 36, 2212 (1987); A.J. McKane, ibid. 49, 12003 (1994).
31. G. Álvarez, V. Martín-Mayor, and J.J. Ruiz-Lorenzo, J. Phys. A 33, 841 (2000).
32. B.N. Shalaev, S.A. Antonenko, and A.I. Sokolov, Phys. Lett. A 230, 105 (1997).
33. R. Folk, Yu. Holovatch, and T. Yavors'kii, Phys. Rev. B 61, 15114 (2000).
34. V. Blavats'ka and Yu. Holovatch, J. Mol. Liq. 105, 221 (2003).
35. A. Pelissetto and E. Vicari, Phys. Rev. B 62, 6393 (2000).
36. 2 = 0.8(1) (Ref. [28])
37. P. Calabrese, P. Parruccini, A. Pelissetto, and E. Vicari, e-print cond-mat/0307699.
38. J.-H. Chen, M.E. Fisher, and B.G. Nickel, Phys. Rev. Lett. 48, 630 (1982).
39. H.G. Ballesteros, L.A. Fernández, V. Martín-Mayor, and A. Muñoz Sudupe, Phys. Lett. B 441, 330 (1998).
40. M. Hasenbusch, K. Pinn, and S. Vinti, Phys. Rev. B 59, 11471 (1999); M. Hasenbusch, J. Phys. A 32, 4851 (1999); 34, 1 (2001).
41. M. Hasenbusch, K. Pinn, and S. Vinti, Phys. Rev. B 59, 11471 (1999); M. Hasenbusch, J. Phys. A 32, 4851 (1999); 34, 1 (2001).
42. M. Hasenbusch, K. Pinn, and S. Vinti, Phys. Rev. B 59, 11471 (1999); M. Hasenbusch, J. Phys. A 32, 4851 (1999); 34, 1 (2001).
43. M. Campostrini, M. Hasenbusch, A. Pelissetto, P. Rossi, and E. Vicari, Phys. Rev. B 63, 214503 (2001); 65, 144520 (2002).
44. M. Campostrini, M. Hasenbusch, A. Pelissetto, P. Rossi, and E. Vicari, Phys. Rev. B 63, 214503 (2001); 65, 144520 (2002).
45. S. Caracciolo, R.G. Edwards, S.J. Ferreira, A. Pelissetto, and A.D. Sokal, Phys. Rev. Lett. 74, 2969 (1995).
46. S. Caracciolo, R.G. Edwards, A. Pelissetto, and A.D. Sokal, Phys. Rev. Lett. 75, 1891 (1995).
47. G. Mana, A. Pelissetto, and A.D. Sokal, Phys. Rev. D 55, 3674 (1997).
48. M. Lüscher, P. Weisz, and U. Wolff, Nucl. Phys. B 359, 221 (1991).
49. J.-K. Kim, Europhys. Lett. 28, 211 (1994); Phys. Rev. D 50, 4663 (1994); Nucl. Phys. B, Proc. Suppl. 34, 702 (1994).
50. J.-K. Kim, Europhys. Lett. 28, 211 (1994); Phys. Rev. D 50, 4663 (1994); Nucl. Phys. B, Proc. Suppl. 34, 702 (1994).
51. J.-K. Kim, Europhys. Lett. 28, 211 (1994); Phys. Rev. D 50, 4663 (1994); Nucl. Phys. B, Proc. Suppl. 34, 702 (1994).
52. B.G. Nickel, in Phase Transitions, edited by M. Lévy, J.C. Le Guillou, and J. Zinn-Justin (Plenum, New York, 1982).
53. A. Pelissetto and E. Vicari, Nucl. Phys. B 519, 626 (1998).
54. P. Calabrese, M. Caselle, A. Celi, A. Pelissetto, and E. Vicari, J. Phys. A 33, 8155 (2000).
55. M. Caselle, A. Pelissetto, and E. Vicari, in Fluctuating Paths and Fields, edited by W. Janke, A. Pelster, H.-J. Schmidt, and M. Bachmann (World Scientific, Singapore, 2001).
56. P. Calabrese, M. De Prato, A. Pelissetto, and E. Vicari, Phys. Rev. B (to be published), e-print cond-mat/0305434.
57. G. Parisi and F. Rapuano, Phys. Lett. 157B, 301 (1985).
58. 32.
59. H.G. Ballesteros, L.A. Fernández, V. Martín-Mayor, A. Muñoz Sudupe, G. Parisi, and J.J. Ruiz-Lorenzo, Nucl. Phys. B 512, 681 (1998).
60. A. Aharony and A.B. Harris, Phys. Rev. Lett. 77, 3700 (1996).
61. M. Palassini and S. Caracciolo, Phys. Rev. Lett. 82, 5128 (1999).
62. max≈0.542719). The choice of the parameters a,b is not crucial and different choices would perform analogously.
63. S. Caracciolo and A. Pelissetto, Phys. Rev. D 58, 105007 (1998).
64. With our definition of §(β,L) the small-z behavior of F§(z) is determined [49] by the small-momentum behavior of the inverse of the two-point function of the fundamental fields. As in the Ising model without disorder (see V. Martín-Mayor, A. Pelissetto, and E. Vicari, Phys. Rev. E 66, 026112 (2002), and references therein), also in the RIM such corrections are extremely tiny [P. Calabrese, V. Martín-Mayor, A. Pelissetto, and E. Vicari (unpublished)].
65. With our definition of §(β,L) the small-z behavior of F§(z) is determined [49] by the small-momentum behavior of the inverse of the two-point function of the fundamental fields. As in the Ising model without disorder (see V. Martín-Mayor, A. Pelissetto, and E. Vicari, Phys. Rev. E 66, 026112 (2002), and references therein), also in the RIM such corrections are extremely tiny [P. Calabrese, V. Martín-Mayor, A. Pelissetto, and E. Vicari (unpublished)].
66. D.V. Pakhnin and A.I. Sokolov, Phys. Rev. B 64, 094407 (2001); D.V. Pakhnin, A.I. Sokolov, and B.N. Shalaev, Pis'ma Zh. Éksp. Teor. Fiz. 75, 459 (2002) [JETP Lett. 75, 387 (2002)].
67. D.V. Pakhnin and A.I. Sokolov, Phys. Rev. B 64, 094407 (2001); D.V. Pakhnin, A.I. Sokolov, and B.N. Shalaev, Pis'ma Zh. Éksp. Teor. Fiz. 75, 459 (2002) [JETP Lett. 75, 387 (2002)].
68. D.V. Pakhnin and A.I. Sokolov, Phys. Rev. B 64, 094407 (2001); D.V. Pakhnin, A.I. Sokolov, and B.N. Shalaev, Pis'ma Zh. Éksp. Teor. Fiz. 75, 459 (2002) [JETP Lett. 75, 387 (2002)].
69. Yu. Holovatch and T. Yavors'kii, J. Stat. Phys. 92, 785 (1998).
70. R. Folk, Yu. Holovatch, and T. Yavors'kii, Pis'ma v Zh. Éksp. Teor. Fiz. 69, 698 (1999) [JETP Lett. 69, 747 (1999)].
71. R. Folk, Yu. Holovatch, and T. Yavors'kii, Pis'ma v Zh. Éksp. Teor. Fiz. 69, 698 (1999) [JETP Lett. 69, 747 (1999)].
72. K.B. Varnashev, Phys. Rev. B 61, 14660 (2000).
73. D.V. Pakhnin and A.I. Sokolov, Phys. Rev. B 61, 15130 (2000).
74. M. Tissier, D. Mouhanna, J. Vidal, and B. Delamotte, Phys. Rev. B 65, 140402 (2002).
75. J.M. Carmona, A. Pelissetto, and E. Vicari, Phys. Rev. B 61, 15136 (2000).
76. In Ref. [26], results are given for the rescaled couplings ū and v̄. The relation is u ≡ 6πū, v ≡ 16πv̄/3