The high temperature region of the Viana-Bray diluted spin glass model

Journal of Statistical Physics

Volumn 115, Issue 1-2, 2004, Pages 531-555

  Guerra, Francesco ^a   Toninelli, Fabio Lucio ^b,c  

^a UNIVERSITÀ DI ROMA LA SAPIENZA   (Italy)

^b EURANDOM   (Netherlands)

^c UNIVERSITY OF ZURICH   (Switzerland)

Author keywords

Diluted spinglasses; Disordered systems; Multi overlaps; Replica symmetry; Viana Bray model

Indexed keywords

EID: 3543014411     PISSN: 00224715     EISSN: None     Source Type: Journal    
DOI: 10.1023/b:joss.0000019815.11115.54     Document Type: Article

References (25)

1. M. Mézard, G. Parisi, and M. A. Virasoro, Spin Glass Theory and Beyond (World Scientific, Singapore, 1987).
2. M. Mézard, G. Parisi, and R. Zecchina, Analytic and algorithmic solution of random satisfiability problems, Science 297:812-815 (2002).
3. S. Franz and M. Leone, Replica bounds for optimization problems and diluted spin systems, J. Stat. Phys. 111:535 (2003).
4. M. Talagrand, The high temperature case of the K-sat problem, Probab. Theory Related Fields 119:187-212 (2001).
5. F. Guerra and F. L. Toninelli, The thermodynamic limit in mean field spin glass models, Comm. Math. Phys. 230:71-79 (2002).
6. F. Guerra, Broken replica symmetry bounds in the mean field spin glass model, Comm. Math. Phys. 233:1-12 (2003).
7. L. Viana and A. J. Bray, Phase diagrams for dilute spin-glasses, J. Phys. C 18:3037-3051 (1985).
8. I. Kanter and H. Sompolinsky, Mean-field theory of spin-glasses with finite coordination number, Phys. Rev. Lett. 58:164 (1987).
9. D. Sherrington and S. Kirkpatrick, Solvable model of a spin-glass, Phys. Rev. Lett. 35: 1792-1796 (1975).
10. F. Guerra and F. L. Toninelli, Quadratic replica coupling for the Sherrington-Kirkpatrick mean field spin glass model, J. Math. Phys. 43:3704-3716 (2002).
11. F. Guerra and F. L. Toninelli, Central limit theorem for fluctuations in the high temperature region of the Sherrington-Kirkpatrick spin glass model, J. Math. Phys. 43:6224-6237 (2002).
12. N. Creignou and H. Daude, Satisfiability threshold for random XOR-CNF formulas, Discr. Appl. Math. 96-97:41-53 (1999).
13. G. Semerjian and L. F. Cugliandolo, Cluster expansions in dilute systems: applications to satisfiability problems and spin glasses, Phys. Rev. E 64:036115 (2001).
14. M. Talagrand, Mean field models for spin glasses: A first course, to appear in Proceedings of the 2000 Saint Flour Summer School in Probability.
15. F. Comets and J. Neveu, The Sherrington-Kirkpatrick model of spin glasses and stochastic calculus: The high temperature case, Comm. Math. Phys. 166:549-564 (1995).
16. M. Talagrand, Spin Glasses: A Challenge for Mathematicians. Cavity and Mean Field Models (Springer-Verlag, 2003).
17. F. Guerra, The cavity method in the mean field spin glass model. Functional representation of the thermodynamic variables, in Advances in Dynamical Systems and Quantum Physics, S. Albeverio et al., eds. (World Scientific, Singapore, 1995).
18. M. Talagrand, Exponential inequalities and replica symmetry breaking for the Sherrington-Kirkpatrick Model, Ann. Probab. 28:1018-1062 (2000).
19. M. Aizenman, J. Lebowitz, and D. Ruelle, Some rigorous results on the Sherrington-Kirkpatrick spin glass model, Comm. Math. Phys. 112:3-20 (1987).
20. R. Monasson and R. Zecchina, Statistical mechanics of the random K-satisfiability model, Phys. Rev. E 56:1357 (1997).
21. M. Talagrand, Concentration of measure and isoperimetric inequalities in product spaces, Publ. Math. I.H.E.S. 81:73-205 (1995).
22. W. Rhee and M. Talagrand, Martingale inequalities and NP-complete problems, Math. Oper. Res. 12:177-181 (1987).
23. F. Ricci-Tersenghi, M. Weigt, and R. Zecchina, Simplest random K-satisfiability problem, Phys. Rev. E 63:026702 (2001).
24. A. Z. Broder, A. M. Frieze, and E. Upfal, On the satisfiability and maximum satisfiability of random 3-CNF formulas, in Proceedings of the 4th Annual ACM-SIAM Symposium on Discrete Algorithms (Association for Computing Machinery, New York, 1993), pp. 322-330.
25. F. Guerra and F. L. Toninelli, The infinite volume limit in generalized mean field disordered models, Markov Process. Related Fields 9:195-207 (2003).