Abstract
For a slightly stronger assumptions on the interaction we give a very transparent proof of Ruelle's result in the language of Poisson integral measure representation for the correlation functions on the configuration space using some kind of cluster expansion in the densities of configurations.
REFERENCES
D. Ruelle, Superstable Interactions in Classical Statistical Mechanics, Comm. Math. Phys. 18:127–159 (1970).
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).
A. L. Rebenko, Poisson measure representation and cluster expansion in classical statistical mechanics, Comm. Math. Phys. 151:427–443 (1993).
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).
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).
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).
R. A. Minlos, Limiting Gibbs' distribution, Funktzional'nyi analiz i ego Prilozheniya 1(2):60–73 (1967).
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).
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).
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.)
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.)
D. Ruelle, Statistical Mechanics, Rigorous Results (Benjamin, New York/Amsterdam, 1963).
D. Petrina, V. Gerasimenko, and P. Malyshev, Mathematical Foundation of Classical Statistical Mechanics. Continuous Systems (Gordon and Breach Science, New York/London/Paris, 1989).
V. Malyshev and R. Minlos, Gibbs Random Fields. The Cluster Expansion Method (Kluwer, Dordrecht, 1991).
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Rebenko, A.L. A New Proof of Ruelle's Superstability Bounds. Journal of Statistical Physics 91, 815–826 (1998). https://doi.org/10.1023/A:1023098131878
Issue Date:
DOI: https://doi.org/10.1023/A:1023098131878