A. L. Rebenko

We prove a theorem that allows to simplify some combinatorial calculations. An example of application of this theorem in statistical mechanics is given.

A detailed analysis of conditions on 2-body interaction potential, which ensure stability, superstability or strong superstability of statistical systems is given. We give a connection between conditions of superstability (strong superstability) and the problem of minimization of Riesz energy in bounded volumes.

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.