Convergence of Mayer and Virial expansions and the Penrose tree-graph identity

TL;DR

This paper improves the known bounds on the convergence radius of Mayer and Virial series for particle systems by introducing a new partition scheme based on minimum spanning trees, enhancing classical results from Penrose, Ruelle, and Lebowitz.

Contribution

It provides significantly tighter lower bounds for the convergence of Mayer and Virial series using a novel tree-graph partition scheme.

Findings

Enhanced convergence bounds for Mayer series

Improved bounds for Virial series

New partition scheme based on minimum spanning trees

Abstract

We establish new lower bounds for the convergence radius of the Mayer series and the Virial series of a continuous particle system interacting via a stable and tempered pair potential. Our bounds considerably improve those given by Penrose and Ruelle in 1963 for the Mayer series and by Lebowitz and Penrose in 1964 for the Virial series. To get our results we exploit the tree-graph identity given by Penrose in 1967 using a new partition scheme based on minumum spanning trees.