Cluster expansion in the canonical ensemble

TL;DR

This paper proves the convergence of the cluster expansion for a particle system in the canonical ensemble at high temperature and low density, offering a more direct derivation of Mayer's virial expansion.

Contribution

It provides a new, more straightforward proof of cluster expansion convergence in the canonical ensemble, avoiding complex combinatorial methods.

Findings

Validates cluster expansion in the canonical ensemble at high temperature and low density.

Shows uniform convergence in volume and reproduces Mayer's virial expansion.

Offers an alternative derivation method avoiding deep combinatorial issues.

Abstract

We consider a system of particles confined in a box $\La\subset\R^d$ interacting via a tempered and stable pair potential. We prove the validity of the cluster expansion for the canonical partition function in the high temperature - low density regime. The convergence is uniform in the volume and in the thermodynamic limit it reproduces Mayer's virial expansion providing an alternative and more direct derivation which avoids the deep combinatorial issues present in the original proof.