A new proof of Ruelle's superstability bounds

Journal of Statistical Physics

Volumn 91, Issue 3-4, 1998, Pages 815-826

  Rebenko, A L ^a  

^a INSTITUTE OF MATHEMATICS   (Ukraine)

Author keywords

Continuous classical system; Poisson measure; Superstability estimates; Thermodynamic limit

Indexed keywords

EID: 0032071788     PISSN: 00224715     EISSN: None     Source Type: Journal    
DOI: 10.1023/a:1023098131878     Document Type: Article

References (14)

1. D. Ruelle, Superstable Interactions in Classical Statistical Mechanics, Comm. Math. Phys. 18:127-159 (1970).
2. R. L. Dobrushin and R. A. Minlos, Existence and continuity of pressure in classical statistical physics, Teorija Verojatn. i jejo Prim. 12:595-618 (1967).
3. A. L. Rebenko, Poisson measure representation and cluster expansion in classical statistical mechanics, Cumm. Math. Phys. 151:427-443 (1993).
4. R. Gielerak and A. L. Rebenko, Poisson field representation in the statistical mechanics of continuous systems, Operator Theory: Advances and Applications 70:219-226 (1994).
5. R. Gielerak and A. L. Rebenko, Poisson integrals representation in the classical statistical mechanics of continuous systems, J. Math. Phys. 37(7):3354-3374 (1996).
6. A. L. Rebenko and G. V. Shchepan'uk, The convergence of cluster expansion for continuous systems with many-body interactions, J. Stat. Phys. 88:665-689 (1997).
7. R. A. Minlos, Limiting Gibbs' distribution, Funktzional'nyi analiz i ego Prilozheniya 1(2):60-73 (1967).
8. J. Frölich and C.-Ed. Pfister, On the Absence of Spontaneous Symmetry Breaking and of Crystalline Ordering in 2-dimensional Systems, Comm. Math. Phys. 81:277-298 (1981).
9. J. Bricmont, K. Kuroda, and J. Lebowitz, First order phase transitions in lattice and Continuous systems: Extensions of Pirogov-Sinai theory, Comm. Math. Phys. 101:501-522 (1985).
10. S. Albeverio, Yu. Kondratiev, and M. Röckner, Analysis and Geometry on Configuration Spaces, Preprint 97-050, Univ. Bielefeld (to be published in J. Funct. Anal.)
11. S. Albeverio, Yu. Kondratiev, and M. Röckner, Analysis and Geometry on Configuration Spaces: The Gibbsian Case. Preprint 97-091, Univ. Bielefeld (to be published in J. Func. Anal.)
12. D. Ruelle, Statistical Mechanics. Rigorous Results (Benjamin, New York/Amsterdam, 1963).
13. D. Petrina, V. Gerasimenko, and P. Malyshev, Mathematical Foundation of Classical Statistical Mechanics. Continuous Systems (Gordon and Breach Science, New York/ London/Paris, 1989).
14. V. Malyshev and R. Minlos, Gibbs Random Fields. The Cluster Expansion Method (Kluwer, Dordrecht, 1991).