On decay of correlations for unbounded spin systems with arbitrary boundary conditions

Journal of Statistical Physics

Volumn 105, Issue 3-4, 2001, Pages 453-482

  Procacci, Aldo ^a,b   Scoppola, Benedetto ^a,b  

^a FEDERAL UNIVERSITY OF MINAS GERAIS   (Brazil)

^b SAPIENZA UNIVERSITY OF ROME   (Italy)

Author keywords

Cluster expansion; Decay of correlations; Unbounded spin systems

Indexed keywords

EID: 0035498175     PISSN: 00224715     EISSN: None     Source Type: Journal    
DOI: 10.1023/A:1012267523688     Document Type: Article

References (27)

1. 1. D. Stroock and B. Zegarliński, On the ergodic properties of Glauber dynamics, J. Statist. Phys. 81:1007-1019 (1995).
2. 2. F. Martinelli and E. Olivieri, Approach to equilibrium of Glauber dynamics in the one phase region. I. The attractive case, Comm. Math. Phys. 161:447-486 (1994). Approach to equilibrium of Glauber dynamics in the one phase region. II. The general case, Comm. Math. Phys. 161:487-514 (1994).
3. 2. F. Martinelli and E. Olivieri, Approach to equilibrium of Glauber dynamics in the one phase region. I. The attractive case, Comm. Math. Phys. 161:447-486 (1994). Approach to equilibrium of Glauber dynamics in the one phase region. II. The general case, Comm. Math. Phys. 161:487-514 (1994).
4. 3. N. Yoshida, The equivalence of the log-Sobolev inequality and a mixing condition for unbounded spin systems on the lattice, Ann. Inst. H. Poincaré Probab. Statist. 37:223-243 (2001).
5. 4. N. Yoshida, The log-Sobolev inequality for weakly coupled lattice fields, Probab. Theory Related Fields 115:1-40 (1999).
6. 5. B. Zegarlinski, The strong decay to equilibrium for the stochastic dynamics of unbounded spin systems on a lattice, Comm. Math. Phys. 175:401-432 (1996).
7. 6. T. Bodineau and B. Helffer, The log-Sobolev inequality for unbounded spin systems, J. Funct. Anal. 166:168-178 (1999).
8. 7. T. Bodineau and B. Helffer, Correlations, Spectral Gap and Log-Sobolev Inequalities for Unbounded Spins Systems. Differential Equations and Mathematical Physics (Birmingham, AL, 1999), pp. 51-66, AMS/IP Stud. Adv. Math., Vol. 16, Amer. Math. Soc., Providence, RI, 2000.
9. 8. M. Ledoux, Logaritmic Sobolev inequalities for unbounded spin systems revisited. Preprint.
10. 9. C. Cammarota, Decay of correlations for infinite range interactions in unbounded spin systems, Comm. Math. Phys. 85:517-528 (1982).
11. 10. H. Kunz, Analiticity and clustering properties of unbounded spin systems, Comm. Math. Phys. 59:53-69 (1978).
12. 11. R. B. Israel and C. R. Nappi, Exponential clustering for long-range integer-spin systems, Comm. Math. Phys. 68:29-37 (1979).
13. 12. J. L. Lebowitz and E. Presutti, Statistical mechanics of systems of unbounded spins, Comm. Math. Phys. 50:195-218 (1976).
14. 13. V. A. Malishev and I. V. Nickolaev, Uniqueness of Gibbs fields via cluster expansion, J. Statist. Phys. 35:375-379 (1984).
15. 14. A. Val. Antoniouk and A. Vic. Antoniouk, Decay of correlations and uniqueness of Gibbs lattice systems with non quadratic interactions, J. Math. Phys. 37:5444-5454 (1996).
16. 15. C. Newman and H. Spohn, The Shiba relation and asymptotic decay in ferromagnetic models. Preprint.
17. 16. S. Albeverio and R. Hoegh-Krohn, Uniqueness and the global Markov property for Euclidean fields, Comm. Math Phys. 68:95-128 (1979).
18. 2 quantum field model with a strong external field, Comm. Math. Phys. 39:63-76 (1974).
19. 18. B. Simon, The Statistical Mechanics of Lattice Gases, Vol. I, Princeton Series in Physics (Princeton University Press, Princeton, NJ, 1993).
20. 19. B. Helffer, Remarks on decay of correlations and Witten Laplacians. - Brascamp-Lieb inequalities and semi-classical analysis - J. Funct. Anal. 155:571-586 (1998). Remarks on decay of correlations and Witten Laplacians. II. Analysis of the dependence on the interaction, Rev. Math. Phys. 11:321-336 (1999). Remarks on decay of correlations and Witten Laplacians. III. Application to logarithmic Sobolev inequalities, Ann. IHP. Statist. 35:483-508 (1999).
21. 19. B. Helffer, Remarks on decay of correlations and Witten Laplacians. - Brascamp-Lieb inequalities and semi-classical analysis - J. Funct. Anal. 155:571-586 (1998). Remarks on decay of correlations and Witten Laplacians. II. Analysis of the dependence on the interaction, Rev. Math. Phys. 11:321-336 (1999). Remarks on decay of correlations and Witten Laplacians. III. Application to logarithmic Sobolev inequalities, Ann. IHP. Statist. 35:483-508 (1999).
22. 19. B. Helffer, Remarks on decay of correlations and Witten Laplacians. - Brascamp-Lieb inequalities and semi-classical analysis - J. Funct. Anal. 155:571-586 (1998). Remarks on decay of correlations and Witten Laplacians. II. Analysis of the dependence on the interaction, Rev. Math. Phys. 11:321-336 (1999). Remarks on decay of correlations and Witten Laplacians. III. Application to logarithmic Sobolev inequalities, Ann. IHP. Statist. 35:483-508 (1999).
23. 20. H. Spohn and W. Zwerger, Decay of the two-point function in one-dimensional O(N) spin models with long-range interactions. J. Statist. Phys. 94:1037-1043 (1999).
24. 21. R. Dobrushin and S. Shlosman, Completely analytical Gibbs fields. Statistical Physics and dynamical systems. Rigorous results. Workshop, Koeszec/Hung., Prog. Phys. 10:371-403 (1985).
25. 22. D. Brydges, A Short Course on Cluster Expansion, Les Houches (1984), K. Osterwalder and R. Stora, eds. (North Holland Press, 1986).
26. 23. G. A. Battle and P. Federbush, A note on cluster expansion, tree graph identity, extra 1/N! factors!!! Lett. Math. Phys. 8:55-57 (1984).
27. 24. A. Procacci, B. N. B. de Lima, and B. Scoppola, A Remark on high temperature polymer expansion for lattice systems with infinite range pair interactions, Lett. Math. Phys. 45: 303-322 (1998).