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# Superstable criterion and superstable bounds for infinite range interaction I: two-body potentials

### Abstract

A continuous infinite system of point particles interacting via two-body infinite-range potential is considered in the framework of classical statistical mecha ics. We propose some new criterion for interaction potentials to be superstable and give a very transparent proof of the Ruelle's uniform bounds for a family of finite volume correlation functions. It gives a possibility to prove that for any temperature and chemical activity there exists at least one Gibbs state. This article is a generalization of the work \cite{Re98} for the case of infinite range interaction potential.

### Article Information

 Title Superstable criterion and superstable bounds for infinite range interaction I: two-body potentials Source Methods Funct. Anal. Topology, Vol. 13 (2007), no. 1, 50-61 MathSciNet MR2308579 Copyright The Author(s) 2007 (CC BY-SA)

### Authors Information

S. N. Petrenko
Faculty of Mechanics and Mathematics, Kyiv National Taras Shevchenko University, Kyiv, Ukraine

A. L. Rebenko
Institute of Mathematics, National Academy of Sciences of Ukraine, 3 Tereshchenkivs'ka, Kyiv, 01601, Ukraine

### Citation Example

S. N. Petrenko and A. L. Rebenko, Superstable criterion and superstable bounds for infinite range interaction I: two-body potentials, Methods Funct. Anal. Topology 13 (2007), no. 1, 50-61.

### BibTex

@article {MFAT378,
AUTHOR = {Petrenko, S. N. and Rebenko, A. L.},
TITLE = {Superstable criterion and superstable bounds for infinite range interaction I: two-body potentials},
JOURNAL = {Methods Funct. Anal. Topology},
FJOURNAL = {Methods of Functional Analysis and Topology},
VOLUME = {13},
YEAR = {2007},
NUMBER = {1},
PAGES = {50-61},
ISSN = {1029-3531},
URL = {http://mfat.imath.kiev.ua/article/?id=378},
}