On Lennard-Jones type potentials and hard-core potentials with an attractive tail

TL;DR

This paper uses the Brydges-Federbush tree identity to derive new bounds on the convergence radius of the Mayer series for gases with Lennard-Jones and similar potentials, enhancing understanding of their statistical mechanics.

Contribution

It introduces novel bounds for the Mayer series convergence radius for particles interacting through Lennard-Jones type potentials using a classical tree graph formula.

Findings

New bounds for Mayer series convergence radius

Application to Lennard-Jones and similar potentials

Improved understanding of gas phase interactions

Abstract

We revisit an old tree graph formula, namely the Brydges-Federbush tree identity, and use it to get new bounds for the convergence radius of the Mayer series for gases of continuous particles interacting via non absolutely summable pair potentials with an attractive tail including Lennard-Jones type pair potentials.