Finite-size scaling in Ising-like systems with quenched random fields: Evidence of hyperscaling violation

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

Volumn 82, Issue 5, 2010, Pages

  Vink, R L C ^a   Fischer, T ^a   Binder, K ^b  

^a UNIVERSITY OF GÖTTINGEN   (Germany)

^b JOHANNES GUTENBERG UNIVERSITY   (Germany)

Author keywords

[No Author keywords available]

Indexed keywords

BREAK DOWN; CRITICAL EXPONENT; CRITICAL POINTS; DEMIXING TRANSITIONS; FINITE SIZE SCALING; HYPERSCALING RELATIONS; INTERFACE FORMATION; ISING-LIKE SYSTEMS; LINEAR EXTENSIONS; NUMERICAL APPROACHES; POWER LAW; RANDOM FIELD ISING MODELS; RANDOM FIELDS; SIMULATION DATA; SYSTEM SIZE; THREE DIMENSIONS; UNIVERSALITY CLASS;

ISING MODEL;

EID: 78651408062     PISSN: 15393755     EISSN: 15502376     Source Type: Journal    
DOI: 10.1103/PhysRevE.82.051134     Document Type: Article

References (65)

1. Y. Imry and S. K. Ma, Phys. Rev. Lett. 35, 1399 (1975). 10.1103/PhysRevLett.35.1399
2. S. F. Edwards and P. W. Anderson, J. Phys. F: Met. Phys. 5, 965 (1975). 10.1088/0305-4608/5/5/017
3. R. B. Stinchcombe, in Dilute Magnetism, Phase Transitions and Critical Phenomena Vol. 7, edited by, C. Domb, and, J. L. Lebowitz, (Academic Press, London, 1983), p. 151.
4. Spin Glasses and Random Fields, edited by, A. P. Young, (World Scientific, Singapore, 1998).
5. K. Binder and W. Kob, Glassy Materials and Disordered Solids: An Introduction to Their Statistical Mechanics (World Scientific, Singapore, 2005).
6. R. L. C. Vink, K. Binder, and H. Löwen, Phys. Rev. Lett. 97, 230603 (2006) 10.1103/PhysRevLett.97.230603
7. R. L. C. Vink, K. Binder, and H. Löwen, J. Phys.: Condens. Matter 20, 404222 (2008). 10.1088/0953-8984/20/40/404222
8. M. E. Fisher, Rev. Mod. Phys. 46, 597 (1974). 10.1103/RevModPhys.46.597
9. J. Zinn-Justin, Phys. Rep. 344, 159 (2001). 10.1016/S0370-1573(00)00126-5
10. K. Binder, Rep. Prog. Phys. 60, 487 (1997). 10.1088/0034-4885/60/5/001
11. K. Binder and E. Luijten, Phys. Rep. 344, 179 (2001). 10.1016/S0370-1573(00)00127-7
12. K. Binder and D. W. Heermann, Monte Carlo Simulation in Statistical Physics: An Introduction, 4th ed. (Springer, Berlin, 2002).
13. M. E. Fisher, in Critical Phenomena, edited by, M. S. Green, (Academic Press, London, 1971), p. 1.
14. Finite Size Scaling and Numerical Simulation of Statistical Systems, edited by, V. Privman, (World Scientific, Singapore, 1990).
15. K. Binder, Z. Phys. B: Condens. Matter 43, 119 (1981). 10.1007/BF01293604
16. K. Binder, Phys. Rev. A 25, 1699 (1982). 10.1103/PhysRevA.25.1699
17. K. Binder and D. P. Landau, Phys. Rev. B 30, 1477 (1984). 10.1103/PhysRevB.30.1477
18. A. Aharony and A. B. Harris, Phys. Rev. Lett. 77, 3700 (1996). 10.1103/PhysRevLett.77.3700
19. S. Wiseman and E. Domany, Phys. Rev. Lett. 81, 22 (1998) 10.1103/PhysRevLett.81.22
20. S. Wiseman and E. Domany, Phys. Rev. E 52, 3469 (1995) 10.1103/PhysRevE.52.3469
21. S. Wiseman and E. Domany, Phys. Rev. E 58, 2938 (1998). 10.1103/PhysRevE.58.2938
22. E. Kierlik, P. A. Monson, M. I. Rosinberg, and G. Tarjus, J. Phys.: Condens. Matter 14, 9295 (2002). 10.1088/0953-8984/14/40/319
23. A. Malakis and N. G. Fytas, Phys. Rev. E 73, 016109 (2006). 10.1103/PhysRevE.73.016109
24. P. E. Berche, C. Chatelain, B. Berche, and W. Janke, Eur. Phys. J. B 38, 463 (2004). 10.1140/epjb/e2004-00141-x
25. J. Z. Imbrie, Phys. Rev. Lett. 53, 1747 (1984). 10.1103/PhysRevLett.53. 1747
26. D. P. Belanger, in Experiments on the Random Field Ising Model, Spin Glasses and Random Fields, edited by, A. P. Young, (World Scientific, Singapore, 1998).
27. J. L. Cardy, Phys. Rev. B 29, 505 (1984) 10.1103/PhysRevB.29.505
28. S. Fishman and A. Aharony, J. Phys. C 12, L729 (1979). 10.1088/0022-3719/12/18/006
29. D. P. Belanger, A. R. King, V. Jaccarino, and J. L. Cardy, Phys. Rev. B 28, 2522 (1983). 10.1103/PhysRevB.28.2522
30. Z. Slanič, D. P. Belanger, and J. A. Fernandez-Baca, Phys. Rev. Lett. 82, 426 (1999). 10.1103/PhysRevLett.82.426
31. H. Rieger, Phys. Rev. B 52, 6659 (1995). 10.1103/PhysRevB.52.6659
32. M. E. J. Newman and G. T. Barkema, Phys. Rev. E 53, 393 (1996). 10.1103/PhysRevE.53.393
33. J. Villain, J. Phys. (France) 46, 1843 (1985). 10.1051/jphys: 0198500460110184300
34. D. S. Fisher, Phys. Rev. Lett. 56, 416 (1986). 10.1103/PhysRevLett.56.416
35. T. Nattermann, in Theory of the Random Field Ising Model, Spin Glasses and Random Fields, edited by, A. P. Young, (World Scientific, Singapore, 1998), p. 277.
36. M. Schwartz, J. Phys. C 18, 135 (1985). 10.1088/0022-3719/18/1/019
37. M. Schwartz, M. Gofman, and T. Nattermann, Physica A 178, 6 (1991). 10.1016/0378-4371(91)90071-J
38. M. Gofman, J. Adler, A. Aharony, A. B. Harris, and M. Schwartz, Phys. Rev. Lett. 71, 1569 (1993). 10.1103/PhysRevLett.71.1569
39. P. C. Hohenberg and B. I. Halperin, Rev. Mod. Phys. 49, 435 (1977). 10.1103/RevModPhys.49.435
40. A. P. Young and M. Nauenberg, Phys. Rev. Lett. 54, 2429 (1985). 10.1103/PhysRevLett.54.2429
41. E. Eichhorn and K. Binder, EPL 30, 331 (1995) 10.1209/0295-5075/30/6/003
42. E. Eichhorn and K. Binder, J. Phys.: Condens. Matter 8, 5209 (1996). 10.1088/0953-8984/8/28/005
43. N. G. Fytas, A. Malakis, and K. Eftaxias, J. Stat. Mech.: Theory Exp. 2008, P03015. 10.1088/1742-5468/2008/03/P03015
44. H. E. Stanley, Introduction to Phase Transitions and Critical Phenomena (Oxford University Press, Oxford, 1971).
45. G. Orkoulas, A. Z. Panagiotopoulos, and M. E. Fisher, Phys. Rev. E 61, 5930 (2000). 10.1103/PhysRevE.61.5930
46. A. K. Hartmann and U. Nowak, Eur. Phys. J. B 7, 105 (1999). 10.1007/s100510050593
47. M. S. Cao and J. Machta, Phys. Rev. B 48, 3177 (1993). 10.1103/PhysRevB.48.3177
48. C. Borgs and R. Kotecký, J. Stat. Phys. 61, 79 (1990). 10.1007/BF01013955
49. N. B. Wilding and A. D. Bruce, J. Phys.: Condens. Matter 4, 3087 (1992). 10.1088/0953-8984/4/12/008
50. E. Luijten, M. E. Fisher, and A. Z. Panagiotopoulos, Phys. Rev. Lett. 88, 185701 (2002). 10.1103/PhysRevLett.88.185701
51. B. Grossmann and M. L. Laursen, Nucl. Phys. B 408, 637 (1993). 10.1016/0550-3213(93)90383-Z
52. J. Lee and J. M. Kosterlitz, Phys. Rev. Lett. 65, 137 (1990). 10.1103/PhysRevLett.65.137
53. C. Borgs and S. Kappler, Phys. Lett. A 171, 37 (1992). 10.1016/0375-9601(92)90129-A
54. G. Orkoulas, M. E. Fisher, and A. Z. Panagiotopoulos, Phys. Rev. E 63, 051507 (2001). 10.1103/PhysRevE.63.051507
55. J. Machta, M. E. J. Newman, and L. B. Chayes, Phys. Rev. E 62, 8782 (2000). 10.1103/PhysRevE.62.8782
56. M. Álvarez, D. Levesque, and J.-J. Weis, Phys. Rev. E 60, 5495 (1999). 10.1103/PhysRevE.60.5495
57. P. G. de Gennes, J. Phys. Chem. 88, 6469 (1984). 10.1021/j150670a004
58. P. G. De Sanctis Lucentini and G. Pellicane, Phys. Rev. Lett. 101, 246101 (2008). 10.1103/PhysRevLett.101.246101
59. R. L. C. Vink, Soft Matter 5, 4388 (2009). 10.1039/b912135h
60. B. Widom and J. S. Rowlinson, J. Chem. Phys. 52, 1670 (1970). 10.1063/1.1673203
61. G. Johnson, H. Gould, J. Machta, and L. K. Chayes, Phys. Rev. Lett. 79, 2612 (1997). 10.1103/PhysRevLett.79.2612
62. R. L. C. Vink, J. Chem. Phys. 124, 094502 (2006). 10.1063/1.2171191
63. F. Wang and D. P. Landau, Phys. Rev. Lett. 86, 2050 (2001). 10.1103/PhysRevLett.86.2050
64. A. M. Ferrenberg and R. H. Swendsen, Phys. Rev. Lett. 61, 2635 (1988). 10.1103/PhysRevLett.61.2635
65. P. Virnau and M. Müller, J. Chem. Phys. 120, 10925 (2004). 10.1063/1.1739216