Statistics of energy levels and zero temperature dynamics for deterministic spin models with glassy behaviour

Journal of Statistical Physics

Volumn 102, Issue 5-6, 2001, Pages 1285-1313

  Degli Esposti, M ^a   Giardina C ^a   Graffi, S ^a   Isola, S ^b  

^a UNIVERSITY OF BOLOGNA   (Italy)

^b UNIVERSITY OF CAMERINO   (Italy)

Author keywords

Deterministic spin glasses; Discrete Fourier transform; Gauss sums; Glauber dynamics; Metastable states; Random octagonal model

Indexed keywords

EID: 0035285794     PISSN: 00224715     EISSN: None     Source Type: Journal    
DOI: 10.1023/A:1004844429584     Document Type: Article

References (23)

1. [KTW] T. R. Kirkpatrick and P. G. Wolynes, Phys. Rev. A 35:3072 (1987); Phys. Rev. B 36:8552 (1987). T. R. Kirkpatrick and D. Thirumalai, Phys. Rev. B 36:5388 (1987): Phys. Rev. B 38:4881 (1988). For a review see also T. R. Kirkpatrick and D. Thirumalai. Transp. Theor. Stat. Phys. 24:927 (1995).
2. [KTW] T. R. Kirkpatrick and P. G. Wolynes, Phys. Rev. A 35:3072 (1987); Phys. Rev. B 36:8552 (1987). T. R. Kirkpatrick and D. Thirumalai, Phys. Rev. B 36:5388 (1987): Phys. Rev. B 38:4881 (1988). For a review see also T. R. Kirkpatrick and D. Thirumalai. Transp. Theor. Stat. Phys. 24:927 (1995).
3. [KTW] T. R. Kirkpatrick and P. G. Wolynes, Phys. Rev. A 35:3072 (1987); Phys. Rev. B 36:8552 (1987). T. R. Kirkpatrick and D. Thirumalai, Phys. Rev. B 36:5388 (1987): Phys. Rev. B 38:4881 (1988). For a review see also T. R. Kirkpatrick and D. Thirumalai. Transp. Theor. Stat. Phys. 24:927 (1995).
4. [KTW] T. R. Kirkpatrick and P. G. Wolynes, Phys. Rev. A 35:3072 (1987); Phys. Rev. B 36:8552 (1987). T. R. Kirkpatrick and D. Thirumalai, Phys. Rev. B 36:5388 (1987): Phys. Rev. B 38:4881 (1988). For a review see also T. R. Kirkpatrick and D. Thirumalai. Transp. Theor. Stat. Phys. 24:927 (1995).
5. [KTW] T. R. Kirkpatrick and P. G. Wolynes, Phys. Rev. A 35:3072 (1987); Phys. Rev. B 36:8552 (1987). T. R. Kirkpatrick and D. Thirumalai, Phys. Rev. B 36:5388 (1987): Phys. Rev. B 38:4881 (1988). For a review see also T. R. Kirkpatrick and D. Thirumalai. Transp. Theor. Stat. Phys. 24:927 (1995).
6. [SW] F. H. Stillinger and T. A. Weber, Science 225:983 (1984).
7. [MP] M. Mézard and G. Parisi, Statistical physics of structural glasses, cond-mat 0002128.
8. [MPR] E. Marinari, G. Parisi, and F. Ritort, J. Phys. A: Math. Gen. 27:7615 (1994): J. Phys. A: Math. Gen. 27:7647 (1994).
9. [MPR] E. Marinari, G. Parisi, and F. Ritort, J. Phys. A: Math. Gen. 27:7615 (1994): J. Phys. A: Math. Gen. 27:7647 (1994).
10. [BM] J. P. Bouchaud and M. Mézard, J. Physique I 4:1109 (1994).
11. [BDGU] I. Borsari, M. Degli Esposti, S. Graffi, and F. Unguendoli, J. Phys. A: Math. Gen. 30: L155 (1997).
12. [NM] M. E. J. Newman and C. Moore, Glassy dynamics and aging in an exactly solvable spin model, Preprint 1997, cond-mat/9707273.
13. [PP] G. Parisi and M. Potters, J. Phys. A:; Math. Gen. 28:5267-5285 (1995).
14. [PP2] G. Parisi and M. Potters, Europhysics Letters 32:13-17 (1995).
15. [MPV] M. Mézard, G. Parisi, and M. Virasoro, Spin Glass Theory and Beyond (World Scientific, Singapore, 1995).
16. [TE] K. Tanaka and S. F. Edwards, J. Phys. F 10:2769 (1980).
17. [BrM] A. J. Bray and M. A. Moore, J. Phys C: Solid State Phys. 13:L469 (1980).
18. [DGGO] C. De Dominicis, M. Gabay, T. Garel, and H. Orland, J. Phys. (Paris) 41:923 (1980).
19. [OF] V. M. De Oliveira and J. F. Fontanari, J. Phys. A: Math. Gen. 30:8445 (1997).
20. [NS] C. M. Newman and D. L. Stein, Metastable states in spin glasses and disordered ferromagnets, Preprint 1999, cond-mat/9908455.
21. [BiM] G. Biroli and R. Monasson, From inherent structures to pure states: Some simple remarks and examples, Preprint 1999, cond-mat/9912061, to appear on Europhys.. Lett.
22. [Ap] T. Apostol, Introduction to Analytic Number Theory (Springer, New York, 1976).
23. [Si] YA. G. Sinai, Probability Theory (Springer-Verlag, 1991).