Numerical Evidence of Infinite Number of Pure States Near Ferromagnetic Phase Boundary for Short-Range Spin-Glass Systems

Journal of the Physical Society of Japan

Volumn 70, Issue 12, 2001, Pages 3471-3474

  Ozeki, Yukiyasu ^a   Ito, Nobuyasu ^b,c   Ogawa, Keita ^a  

^a TOKYO INSTITUTE OF TECHNOLOGY   (Japan)

^b INSTITUTE OF STATISTICAL MATHEMATICS   (Japan)

^c UNIVERSITY OF TOKYO   (Japan)

Author keywords

J Ising model; Gauge glass; Multivalley; Nonequilibrium relaxation; Spin glass

Indexed keywords

EID: 0035564546     PISSN: 00319015     EISSN: None     Source Type: Journal    
DOI: 10.1143/JPSJ.70.3471     Document Type: Article

References (39)

1. K. Binder and A. P. Young: Rev. Mod. Phys. 58 (1986) 801.
2. M. Mezard, G. Parisi and A. Virasoro: Spin Glass Theory and Beyond (World Scientific, Singapore, 1987).
3. S. F. Edwards and P. W. Anderson: J. Phys. F 5 (1975) 965.
4. D. Sherrington and S. Kirkpatrick: Phys. Rev. Lett. 35 (1975) 1792.
5. G. Parisi: Phys. Rev. Lett. 43 (1979) 1754.
6. D. Stauffer: Physica A 186 (1992) 197.
7. G. A. Kohring and D. Stauffer: Int. J. Mod. Phys. C 3 (1992) 1165.
8. N. Ito: Physica A 192 (1993) 591.
9. N. Ito: Physica A 196 (1993) 604.
10. N. Ito, T. Matsuhisa and H. Kitatani: J. Phys. Soc. Jpn. 67 (1998) 1188.
11. Y. Ozeki and N. Ito: J. Phys. A 31 (1998) 5451.
12. N. Ito, Y. Ozeki and H. Kitatani: J. Phys. Soc. Jpn. 68 (1999) 803.
13. N. Ito, K. Hukushima, K. Ogawa and Y. Ozeki: J. Phys. Soc. Jpn. 69 (2000) 1931.
14. Y. Ozeki and N. Ito: Phys. Rev. B 64 (2001) 024416.
15. H. Nishimori: Prog. Theor. Phys. 66 (1981) 1169.
16. H. Kitatani: J. Phys. Soc. Jpn. 61 (1992) 4049.
17. Y. Ozeki and H. Nishimori: J. Phys. A 26 (1993) 3399.
18. Y. Ozeki: J. Phys. A 28 (1995) 3645.
19. Y. Ozeki: J. Phys.: Condens. Matter 9 (1997) 11171.
20. H. Nishimori and D. Sherrington: cond-mat/0008139.
21. M. Suzuki: Phys. Lett. A 58 (1976) 435.
22. M. Suzuki: Prog. Theor. Phys. 58 (1977) 1142.
23. S. Jain and A. P. Young: J. Phys. C 19 (1986) 3913.
24. B. M. Morris, S. G. Colborne, M. A. Moore, A. J. Bray and J. Canisius: J. Phys. C 19 (1986) 1157.
25. Y. Ozeki and H. Nishimori: Phys. Rev. B 46 (1992) 2879.
26. D. A. Huse and H. S. Seung: Phys. Rev. B 42 (1990) 1059.
27. J. D. Reger, T. A. Tokuyasu, A. P. Young and M. P. A. Fisher: Phys. Rev. B 44 (1991) 7147.
28. C. Wengel and A. P. Young: Phys. Rev. B 56 (1997) 5918.
29. J. Maucourt and D. R. Grempel: Phys. Rev. B 58 (1998) 2654.
30. J. M. Kosterlitz and N. Akino: Phys. Rev. Lett. 81 (1998) 4672.
31. For example, let us compare the data m(t) for the ±J Ising model with t = 20000 at p = 0.7672 on the Nishimori line, which is very close to the MCP; it is the most severe case. We use the estimation m(t) = 0.2418(2) of the 161 × 161 × 162 lattice for the analysis. It is also estimated to be within the error bar for 361 and 451 lattices. Similar accuracies are achieved for other parameters. With such accuracy, our estimations of local exponents are almost identical for these lattices and it is difficult to identify a systematic size dependence.
32. 15) However, it is insufficient to neglect the phase observed by the NER analysis. Thus, we simply use "FM-LRO" for eq. (7).
33. When the initial state is far from equilibrium, the system tends to be trapped at a local minimum in a short time scale. Such an effect is not so serious for the analysis in the FM phase, since the initial and final states are both ferromagnetic. In the non-FM region, i.e., the SG phase in the presentanalysis, even if the system is trapped at local minimum states, the time scale for such trapping depends on the random realization and is distributed widely within the short time scale. We expect that this effect does not provide a macroscopic behavior at a definite time scale which could mislead us as to the FM behavior, but instead provides an intrinsic slow dynamics typical in SG systems.
34. Y. Ozeki and H. Nishimori: J. Phys. Soc. Jpn. 56 (1987) 3265.
35. M. J. P. Gingras and S. Sørensen: Phys. Rev. B 46 (1992) 3441.
36. T. Nattermann, S. Scheidl, S. E. Korshunov and M. S. Li: J. Phys. I (Paris) 5 (1995) 565.
37. M.-C. Cha and H. A. Fertig: Phys. Rev. Lett. 74 (1995) 4867.
38. R. N. Bhatt and A. P. Young: Phys. Rev. Lett. 54 (1985) 924.
39. R. R. P. Singh and S. Chakravarty: Phys. Rev. Lett. 57 (1986) 245.