Quasi-lattice approximation of statistical systems with strong superstable interactions. Correlation functions

TL;DR

This paper introduces a quasi-lattice approximation method for infinite particle systems with strong superstable interactions, showing convergence of pressure and correlation functions as the approximation parameter approaches zero.

Contribution

It develops a new approximation framework for statistical systems with superstable potentials, demonstrating convergence of key thermodynamic quantities.

Findings

Pressure of the approximated system converges to the original system's pressure as the parameter a approaches zero.

Correlation functions of the approximated system converge to those of the original system for small activity z.

The method applies to systems with strong superstable interactions across all inverse temperatures.

Abstract

A continuous infinite system of point particles interacting via two-body strong superstable potential is considered in the framework of classical statistical mechanics. We define some kind of approximation of main quantities, which describe macroscopical and microscopical characteristics of systems, such as grand partition function and correlation functions. The pressure of an approximated system converge to the pressure of the initial system if the parameter of approximation $a\to 0$ for any values of an inverse temperature $\beta >0$ and a chemical activity $z$. The same result is true for the family of correlation functions in the region of small z