Crossover behavior in three-dimensional dilute spin systems

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

Volumn 69, Issue 3 2, 2004, Pages

  Calabrese, Pasquale ^a   Parruccini, Pietro ^b   Pelissetto, Andrea ^c   Vicari, Ettore ^b  

^a INFN SEZIONE DI PISA   (Italy)

^b UNIVERSITY OF PISA   (Italy)

^c UNIVERSITÀ DI ROMA LA SAPIENZA   (Italy)

Author keywords

[No Author keywords available]

Indexed keywords

ASYMPTOTIC STABILITY; HAMILTONIANS; IMPURITIES; MAGNETIC FIELDS; MAGNETIC SUSCEPTIBILITY; MATHEMATICAL MODELS; MONTE CARLO METHODS; POROUS MATERIALS; RANDOM PROCESSES;

HEISENBERG SYSTEMS; QUARTIC COUPLING; SPIN SYSTEMS;

MAGNETIC MATERIALS;

EID: 42749105234     PISSN: 1063651X     EISSN: None     Source Type: Journal    
DOI: 10.1103/PhysRevE.69.036120     Document Type: Article

References (74)

1. 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.
2. R. B. Stinchcombe, in Phase Transitions and Critical Phenomena, edited by C. Domb and J. Lebowitz (Academic Press, New York, 1983), Vol. 7, p. 152.
3. D.P. Belanger, Braz. J. Phys. 30, 682 (2000).
4. A. Pelissetto and E. Vicari, Phys. Rep. 368, 549 (2002).
5. R. Folk, Yu. Holovatch, and T. Yavors'kii, Usp. Fiz. Nauk 173, 175 (2003) [Phys. Usp. 46, 175 (2003)].
6. R. Folk, Yu. Holovatch, and T. Yavors'kii, Usp. Fiz. Nauk 173, 175 (2003) [Phys. Usp. 46, 175 (2003)].
7. cr corresponds to a multicritical point [J.M. Kosterlitz, D.R. Nelson, and M.E. Fisher, Phys. Rev. Lett. 33, 813 (1974); Phys. Rev. B 13, 412 (1976)]. On the other hand, in the presence of dilution, for any H≠0 the transition does not belong to the RIM universality class but rather to the same universality class of the transition of the random-field Ising model. See S. Fishman and A. Aharony, J. Phys. C 12, L729 (1979); D. P. Belanger, in Spin Glasses and Random Fields, edited by A. P. Young (World Scientific, Singapore, 1998), p. 251. The crossover exponent that controls the behavior in the limit H→0 has been recently estimated by computing and analyzing six-loop series in the framework of the fixed-dimension FT expansion [P. Calabrese, A. Pelissetto, and E. Vicari, Phys. Rev. B 68, 092409 (2003)].
8. cr corresponds to a multicritical point [J.M. Kosterlitz, D.R. Nelson, and M.E. Fisher, Phys. Rev. Lett. 33, 813 (1974); Phys. Rev. B 13, 412 (1976)]. On the other hand, in the presence of dilution, for any H≠0 the transition does not belong to the RIM universality class but rather to the same universality class of the transition of the random-field Ising model. See S. Fishman and A. Aharony, J. Phys. C 12, L729 (1979); D. P. Belanger, in Spin Glasses and Random Fields, edited by A. P. Young (World Scientific, Singapore, 1998), p. 251. The crossover exponent that controls the behavior in the limit H→0 has been recently estimated by computing and analyzing six-loop series in the framework of the fixed-dimension FT expansion [P. Calabrese, A. Pelissetto, and E. Vicari, Phys. Rev. B 68, 092409 (2003)].
9. cr corresponds to a multicritical point [J.M. Kosterlitz, D.R. Nelson, and M.E. Fisher, Phys. Rev. Lett. 33, 813 (1974); Phys. Rev. B 13, 412 (1976)]. On the other hand, in the presence of dilution, for any H≠0 the transition does not belong to the RIM universality class but rather to the same universality class of the transition of the random-field Ising model. See S. Fishman and A. Aharony, J. Phys. C 12, L729 (1979); D. P. Belanger, in Spin Glasses and Random Fields, edited by A. P. Young (World Scientific, Singapore, 1998), p. 251. The crossover exponent that controls the behavior in the limit H→0 has been recently estimated by computing and analyzing six-loop series in the framework of the fixed-dimension FT expansion [P. Calabrese, A. Pelissetto, and E. Vicari, Phys. Rev. B 68, 092409 (2003)].
10. cr corresponds to a multicritical point [J.M. Kosterlitz, D.R. Nelson, and M.E. Fisher, Phys. Rev. Lett. 33, 813 (1974); Phys. Rev. B 13, 412 (1976)]. On the other hand, in the presence of dilution, for any H≠0 the transition does not belong to the RIM universality class but rather to the same universality class of the transition of the random-field Ising model. See S. Fishman and A. Aharony, J. Phys. C 12, L729 (1979); D. P. Belanger, in Spin Glasses and Random Fields, edited by A. P. Young (World Scientific, Singapore, 1998), p. 251. The crossover exponent that controls the behavior in the limit H→0 has been recently estimated by computing and analyzing six-loop series in the framework of the fixed-dimension FT expansion [P. Calabrese, A. Pelissetto, and E. Vicari, Phys. Rev. B 68, 092409 (2003)].
11. cr corresponds to a multicritical point [J.M. Kosterlitz, D.R. Nelson, and M.E. Fisher, Phys. Rev. Lett. 33, 813 (1974); Phys. Rev. B 13, 412 (1976)]. On the other hand, in the presence of dilution, for any H≠0 the transition does not belong to the RIM universality class but rather to the same universality class of the transition of the random-field Ising model. See S. Fishman and A. Aharony, J. Phys. C 12, L729 (1979); D. P. Belanger, in Spin Glasses and Random Fields, edited by A. P. Young (World Scientific, Singapore, 1998), p. 251. The crossover exponent that controls the behavior in the limit H→0 has been recently estimated by computing and analyzing six-loop series in the framework of the fixed-dimension FT expansion [P. Calabrese, A. Pelissetto, and E. Vicari, Phys. Rev. B 68, 092409 (2003)].
12. P. Calabrese, V. Martín-Mayor, A. Pelissetto, and E. Vicari, Phys. Rev. E 68, 036136 (2003).
13. H.G. Ballesteros, L.A. Fernández, V. Martín-Mayor, A. Muñoz Sudupe, G. Parisi, and J.J. Ruiz-Lorenzo, Phys. Rev. B 58, 2740 (1998).
14. S. Wiseman and E. Domany, Phys. Rev. Lett. 81, 22 (1998); Phys. Rev. E 58, 2938 (1998).
15. S. Wiseman and E. Domany, Phys. Rev. Lett. 81, 22 (1998); Phys. Rev. E 58, 2938 (1998).
16. W. Selke, L. N. Shchur, and A. L. Talapov, in Annual Reviews of Computational Physics, edited by D. Stauffer (World Scientific, Singapore, 1995), Vol. I.
17. A. Pelissetto and E. Vicari, Phys. Rev. B 62, 6393 (2000).
18. P. Calabrese, A. Pelissetto, P. Rossi, and E. Vicari, Int. J. Mod. Phys. B 17, 5829 (2003); Talk at the International Conference on Theoretical Physics, TH-2002, UNESCO, Paris, 2002.
19. P. Calabrese, A. Pelissetto, P. Rossi, and E. Vicari, Int. J. Mod. Phys. B 17, 5829 (2003); Talk at the International Conference on Theoretical Physics, TH-2002, UNESCO, Paris, 2002.
20. D.V. Pakhnin and A.I. Sokolov, Phys. Rev. B 61, 15 130 (2000).
21. R. Folk, Yu. Holovatch, and T. Yavors'kii, Phys. Rev. B 61, 15 114 (2000).
22. B.N. Shalaev, S.A. Antonenko, and A.I. Sokolov, Phys. Lett. A 230, 105 (1997).
23. M. Tissier, D. Mouhanna, J. Vidal, and B. Delamotte, Phys. Rev. B 65, 14 0402 (2002).
24. A.B. Harris, J. Phys. C 7, 1671 (1974).
25. M. Campostrini, M. Hasenbusch, A. Pelissetto, P. Rossi, and E. Vicari, Phys. Rev. B 63, 214503 (2001).
26. M. Campostrini, M. Hasenbusch, A. Pelissetto, P. Rossi, and E. Vicari, Phys. Rev. B 65, 144520 (2002).
27. J. Yoon and M.H.W. Chan, Phys. Rev. Lett. 78, 4801 (1997).
28. G.M. Zassenhaus and J.D. Reppy, Phys. Rev. Lett. 83, 4800 (1999).
29. S.N. Kaul, J. Magn. Magn. Mater. 53, 5 (1985).
30. S.N. Kaul and M. Sambasiva Rao, J. Phys.: Condens. Matter 6, 7403 (1994).
31. P.D. Babu and S.N. Kaul, J. Phys.: Condens. Matter 9, 7189 (1997).
32. V.L. Ginzburg, Fiz. Tverd. Tela 2, 2031 (1960) [Sov. Phys. Solid State 2, 1824 (1960)].
33. V.L. Ginzburg, Fiz. Tverd. Tela 2, 2031 (1960) [Sov. Phys. Solid State 2, 1824 (1960)].
34. E. Luijten and K. Binder, Phys. Rev. E 58, R4060 (1998); 59, 7254 (1999); A. Pelissetto, P. Rossi, and E. Vicari, ibid. 58, 7146 (1998); Nucl. Phys. B 554, 552 (1999); S. Caracciolo, M.S. Causo, A. Pelissetto, P. Rossi, and E. Vicari, Phys. Rev. E 64, 046130 (2001).
35. E. Luijten and K. Binder, Phys. Rev. E 58, R4060 (1998); 59, 7254 (1999); A. Pelissetto, P. Rossi, and E. Vicari, ibid. 58, 7146 (1998); Nucl. Phys. B 554, 552 (1999); S. Caracciolo, M.S. Causo, A. Pelissetto, P. Rossi, and E. Vicari, Phys. Rev. E 64, 046130 (2001).
36. E. Luijten and K. Binder, Phys. Rev. E 58, R4060 (1998); 59, 7254 (1999); A. Pelissetto, P. Rossi, and E. Vicari, ibid. 58, 7146 (1998); Nucl. Phys. B 554, 552 (1999); S. Caracciolo, M.S. Causo, A. Pelissetto, P. Rossi, and E. Vicari, Phys. Rev. E 64, 046130 (2001).
37. E. Luijten and K. Binder, Phys. Rev. E 58, R4060 (1998); 59, 7254 (1999); A. Pelissetto, P. Rossi, and E. Vicari, ibid. 58, 7146 (1998); Nucl. Phys. B 554, 552 (1999); S. Caracciolo, M.S. Causo, A. Pelissetto, P. Rossi, and E. Vicari, Phys. Rev. E 64, 046130 (2001).
38. E. Luijten and K. Binder, Phys. Rev. E 58, R4060 (1998); 59, 7254 (1999); A. Pelissetto, P. Rossi, and E. Vicari, ibid. 58, 7146 (1998); Nucl. Phys. B 554, 552 (1999); S. Caracciolo, M.S. Causo, A. Pelissetto, P. Rossi, and E. Vicari, Phys. Rev. E 64, 046130 (2001).
39. C. Bagnuls and C. Bervillier, Phys. Rev. B 32, 7209 (1985); Phys. Rev. E 65, 066132 (2002).
40. C. Bagnuls and C. Bervillier, Phys. Rev. B 32, 7209 (1985); Phys. Rev. E 65, 066132 (2002).
41. R. Schloms and V. Dohm, Nucl. Phys. B 328, 639 (1989).
42. H.J. Krause, R. Schloms, and V. Dohm, Z. Phys. B: Condens. Matter 79, 287 (1990).
43. H.K. Janssen, K. Oerding, and E. Sengespeick, J. Phys. A 28, 6073 (1995).
44. M. Dudka, R. Folk, Yu. Holovatch, and D. Ivaneiko, J. Magn. Magn. Mater. 256, 243 (2003).
45. V.J. Emery, Phys. Rev. B 11, 239 (1975).
46. S.W. Edwards and P.W. Anderson, J. Phys. F: Met. Phys. 5, 965 (1975).
47. G. Grinstein and A. Luther, Phys. Rev. B 13, 1329 (1976).
48. A. Aharony, Y. Imry, and S.K. Ma, Phys. Rev. B 13, 466 (1976).
49. D. Mukamel and G. Grinstein, Phys. Rev. B 25, 381 (1982).
50. J.M. Carmona, A. Pelissetto, and E. Vicari, Phys. Rev. B 61, 15136 (2000).
51. P. Calabrese, A. Pelissetto, and E. Vicari, Phys. Rev. B 67, 024418 (2003).
52. 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, 12 003 (1994).
53. 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, 12 003 (1994).
54. G. Álvarez, V. Martín-Mayor, and J.J. Ruiz-Lorenzo, J. Phys. A 33, 841 (2000).
55. P. Calabrese, M. De Prato, A. Pelissetto, and E. Vicari, Phys. Rev. B 68, 134418 (2003).
56. 2 at the field-theoretical estimate of the FP.
57. M. Campostrini, A. Pelissetto, P. Rossi, and E. Vicari, Phys. Rev. E 65, 066127 (2002); 60, 3526 (1999).
58. M. Campostrini, A. Pelissetto, P. Rossi, and E. Vicari, Phys. Rev. E 65, 066127 (2002); 60, 3526 (1999).
59. P. Butera and M. Comi, Phys. Rev. B 65, 144431 (2002).
60. J. Kyriakidis and D.J.W. Geldart, Phys. Rev. B 53, 11572 (1996).
61. A. Pelissetto and E. Vicari, Nucl. Phys. B 575, 579 (2000).
62. B. G. Nickel, in Phase Transitions, edited by M. Lévy, J. C. Le Guillou, and J. Zinn-Justin (Plenum, New York-London, 1982).
63. A.D. Sokal, Europhys. Lett. 27, 661 (1994); 30, 123(E) (1995).
64. A.D. Sokal, Europhys. Lett. 27, 661 (1994); 30, 123(E) (1995).
65. A. Pelissetto and E. Vicari, Nucl. Phys. B 519, 626 (1998).
66. A.J. Liu and M.E. Fisher, J. Stat. Phys. 58, 431 (1990).
67. B.J. Nickel, Macromolecules 24, 1358 (1991).
68. L. Schäfer, Phys. Rev. E 50, 3517 (1994).
69. H.G. Ballesteros, L.A. Fernández, V. Martín-Mayor, A. Muñoz Sudupe, G. Parisi, and J.J. Ruiz-Lorenzo, J. Phys. A 32, 1 (1999).
70. This is essentially the argument of Sokal (Ref. [48]) for the nonanalyticity of the β function at a FP. A numerical example illustrating these ideas is given in Appendix E of B. Li, N. Madras, and A.D. Sokal, J. Stat. Phys. 80, 661 (1995).
71. -1(u,v) = 0, where Z, has been defined in Eq. (2.5), or equivalently by the fact that along it % and f diverge [P. Parruccini and P. Rossi, Phys. Rev. E 64, 047104 (2001)].
72. Y. Deng and H.W.J. Blöte, Phys. Rev. E 68, 036125 (2003).
73. R. Guida and J. Zinn-Justin, J. Phys. A 31, 8103 (1998).
74. F. J. Wegner, in Phase Transitions and Critical Phenomena, edited by C. Domb and M. S. Green (Academic Press, New York, 1976), Vol. 6.