Universality of the glassy transitions in the two-dimensional ±j Ising model

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

Volumn 82, Issue 2, 2010, Pages

  Parisen Toldin, Francesco ^a,d   Pelissetto, Andrea ^b   Vicari, Ettore ^c  

^a MAX PLANCK INSTITUTE FOR INTELLIGENT SYSTEMS   (Germany)

^b INFN SEZIONE DI ROMA   (Italy)

^c INFN SEZIONE DI PISA   (Italy)

^d UNIVERSITY OF STUTTGART   (Germany)

Author keywords

[No Author keywords available]

Indexed keywords

BASIC VARIABLES; BIMODAL DISTRIBUTION; CRITICAL BEHAVIOR; FERROMAGNETIC TRANSITIONS; FINITE SIZE SCALING; FINITE VOLUME; FREEZING PHENOMENA; GLASSY SYSTEMS; HAMILTONIAN SPECTRUM; ISING SPIN GLASS; LOW TEMPERATURES; MAGNETIC MODES; MONTE CARLO SIMULATION; RENORMALIZATION GROUP; SQUARE-LATTICE; TRANSITION LINES; ZERO TEMPERATURES;

COMPUTER SIMULATION; FERROMAGNETIC MATERIALS; FERROMAGNETISM; MONTE CARLO METHODS; PARAMAGNETIC MATERIALS; SPIN GLASS;

ISING MODEL;

EID: 77955561823     PISSN: 15393755     EISSN: 15502376     Source Type: Journal    
DOI: 10.1103/PhysRevE.82.021106     Document Type: Article

References (47)

1. S. F. Edwards and P. W. Anderson, J. Phys. F: Met. Phys. 5, 965 (1975). 10.1088/0305-4608/5/5/017
2. H. Nishimori, Statistical Physics of Spin Glasses and Information Processing: An Introduction (Oxford University Press, Oxford, 2001). 10.1093/acprof:oso/9780198509417.001.0001
3. N. Kawashima and H. Rieger, in Frustrated Spin Systems, edited by, H. T. Diep, (World Scientific, Singapore, 2004), 539
4. e-print arXiv:cond-mat/0312432.
5. F. Parisen Toldin, A. Pelissetto, and E. Vicari, J. Stat. Phys. 135, 1039 (2009). 10.1007/s10955-009-9705-5
6. C. Wang, J. Harrington, and J. Preskill, Ann. Phys. (N.Y.) 303, 31 (2003). 10.1016/S0003-4916(02)00019-2
7. C. Amoruso and A. K. Hartmann, Phys. Rev. B 70, 134425 (2004). 10.1103/PhysRevB.70.134425
8. H. Nishimori, Prog. Theor. Phys. 66, 1169 (1981). 10.1143/PTP.66.1169
9. The Nishimori line is defined by the equation T = T N (p) = 2 / [ln p - ln (1 - p)]. Along this line several rigorous results can be proved, such as the equality of the magnetic and overlap two-point correlations.
10. H. Nishimori and K. Nemoto, J. Phys. Soc. Jpn. 71, 1198 (2002). 10.1143/JPSJ.71.1198
11. M. Ohzeki, Phys. Rev. E 79, 021129 (2009). 10.1103/PhysRevE.79.021129
12. P. Le Doussal and A. B. Harris, Phys. Rev. B 40, 9249 (1989) 10.1103/PhysRevB.40.9249
13. P. Le Doussal and A. B. Harris, Phys. Rev. Lett. 61, 625 (1988). 10.1103/PhysRevLett.61.625
14. M. Hasenbusch, F. Parisen Toldin, A. Pelissetto, and E. Vicari, Phys. Rev. E 77, 051115 (2008). 10.1103/PhysRevE.77.051115
15. M. Hasenbusch, F. Parisen Toldin, A. Pelissetto, and E. Vicari, Phys. Rev. E 78, 011110 (2008). 10.1103/PhysRevE.78.011110
16. W. L. McMillan, Phys. Rev. B 29, 4026 (1984). 10.1103/PhysRevB.29.4026
17. The presence of two different universality classes along the paramagnetic-ferromagnetic transition line is neither peculiar of the ± J model nor is it restricted to two dimensions. For instance, approximate RG calculations suggest that a similar phenomenon occurs in the three-dimensional Blume-Emery-Griffiths model with bond randomness [A. Falicov and A. N. Berker, Phys. Rev. Lett. 76, 4380 (1996)]. 10.1103/PhysRevLett.76.4380
18. G. Migliorini and A. N. Berker, Phys. Rev. B 57, 426 (1998). 10.1103/PhysRevB.57.426
19. H. Rieger, L. Santen, U. Blasum, M. Diehl, M. Jünger, and G. Rinaldi, J. Phys. A 29, 3939 (1996) 10.1088/0305-4470/29/14/018
20. H. Rieger, L. Santen, U. Blasum, M. Diehl, M. Jünger, and G. Rinaldi, J. Phys. A 30, 8795 (E) (1997). 10.1088/0305-4470/30/24/038
21. J. Houdayer, Eur. Phys. J. B 22, 479 (2001). 10.1007/PL00011151
22. In the parallel-tempering runs, we divided the interval between T min and T max in N T - 1 intervals chosen so that the exchange acceptance between adjacent temperatures is roughly constant. Typically we had: N T = 3 for L = 8, N T = 3 - 4 for L = 12, N T = 4 - 5 for L = 16, N T = 8 for L = 24, N T = 12 and 26 for L = 32, N T = 9, 10, 11, and 33 for L = 48, and N T = 12, 14, and 33 for L = 64.
23. A. K. Hartmann and A. P. Young, Phys. Rev. B 64, 180404 (R) (2001). 10.1103/PhysRevB.64.180404
24. A. C. Carter, A. J. Bray, and M. A. Moore, Phys. Rev. Lett. 88, 077201 (2002). 10.1103/PhysRevLett.88.077201
25. C. Amoruso, E. Marinari, O. C. Martin, and A. Pagnani, Phys. Rev. Lett. 91, 087201 (2003). 10.1103/PhysRevLett.91.087201
26. J. Lukic, A. Galluccio, E. Marinari, O. C. Martin, and G. Rinaldi, Phys. Rev. Lett. 92, 117202 (2004). 10.1103/PhysRevLett.92.117202
27. J. Houdayer and A. K. Hartman, Phys. Rev. B 70, 014418 (2004). 10.1103/PhysRevB.70.014418
28. H. G. Katzgraber, L. W. Lee, and A. P. Young, Phys. Rev. B 70, 014417 (2004). 10.1103/PhysRevB.70.014417
29. H. G. Katzgraber and L. W. Lee, Phys. Rev. B 71, 134404 (2005). 10.1103/PhysRevB.71.134404
30. T. Jörg, J. Lukic, E. Marinari, and O. C. Martin, Phys. Rev. Lett. 96, 237205 (2006). 10.1103/PhysRevLett.96.237205
31. H. G. Katzgraber, L. W. Lee, and I. A. Campbell, Phys. Rev. B 75, 014412 (2007). 10.1103/PhysRevB.75.014412
32. A. K. Hartmann, Phys. Rev. B 77, 144418 (2008). 10.1103/PhysRevB.77. 144418
33. M. Ohzeki and H. Nishimori, J. Phys. A: Math. Theor. 42, 332001 (2009). 10.1088/1751-8113/42/33/332001
34. The most accurate estimates of ν have been obtained by computing the stiffness exponent θ = - 1 / ν at T = 0 in models with continuous distributions. We mention θ = - 0.281 (2) (Ref.), θ = - 0.282 (2) (Ref.), θ = - 0.282 (3) (Ref.), and θ = - 0.282 (4) (Ref.) obtained by using the Ising glass model with a Gaussian distribution for the couplings, and θ = - 0.275 (5) [F. Liers, J. Lukic, E. Marinari, A. Pelissetto, and E. Vicari, Phys. Rev. B 76, 174423 (2007) 10.1103/PhysRevB.76.174423
35. G. Toulouse, J. Phys. Lett. 41, 447 (1980). 10.1051/jphyslet: 019800041018044700
36. M. Hasenbusch, A. Pelissetto, and E. Vicari, Phys. Rev. B 78, 214205 (2008) 10.1103/PhysRevB.78.214205
37. M. Hasenbusch, A. Pelissetto, and E. Vicari, J. Stat. Mech.: Theory Exp. (2008), L02001. 10.1088/1742-5468/2008/02/L02001
38. J. W. Landry and S. N. Coppersmith, Phys. Rev. B 65, 134404 (2002). 10.1103/PhysRevB.65.134404
39. K. Binder and A. P. Young, Rev. Mod. Phys. 58, 801 (1986). 10.1103/RevModPhys.58.801
40. C. J. Geyer, in Computer Science and Statistics, Proceedings of the 23rd Symposium on the Interface, edited by, E. M. Keramidas, (Interface Foundation, Fairfax Station, 1991), p. 156
41. K. Hukushima and K. Nemoto, J. Phys. Soc. Jpn. 65, 1604 (1996) 10.1143/JPSJ.65.1604
42. D. J. Earl and M. W. Deem, Phys. Chem. Chem. Phys. 7, 3910 (2005). 10.1039/b509983h
43. T. Jörg and F. Ricci-Tersenghi, Phys. Rev. Lett. 100, 177203 (2008). 10.1103/PhysRevLett.100.177203
44. S. Caracciolo, R. G. Edwards, S. J. Ferreira, A. Pelissetto, and A. D. Sokal, Phys. Rev. Lett. 74, 2969 (1995). 10.1103/PhysRevLett.74.2969
45. T. Jörg and H. G. Katzgraber, Phys. Rev. Lett. 101, 197205 (2008). 10.1103/PhysRevLett.101.197205
46. M. Picco, A. Honecker, and P. Pujol, J. Stat. Mech.: Theory Exp. (2006), P09006. 10.1088/1742-5468/2006/09/P09006
47. V. Alba, A. Pelissetto, and E. Vicari, J. Stat. Mech.: Theory Exp. (2010), P03006. 10.1088/1742-5468/2010/03/P03006