The Mayer series of the Lennard-Jones gas: improved bounds for the convergence radius

TL;DR

This paper improves the lower bound for the convergence radius of the Mayer series in the Lennard-Jones gas by combining recent estimates and methods for stable potentials and minimal interatomic distances.

Contribution

It introduces a novel approach that combines recent estimates and optimization methods to significantly improve convergence bounds for the Lennard-Jones gas.

Findings

New lower bound for the convergence radius of the Mayer series

Improved bounds are significantly better than classical results

Method applicable to other stable and tempered potentials

Abstract

We provide a lower bound for the convergence radius of the Mayer series of the Lennard-Jones gas which strongly improves on the classical bound obtained by Penrose and Ruelle 1963. To obtain this result we use an alternative estimate recently proposed by Morais et al. (J. Stat. Phys. 2014) for a restricted class of stable and tempered pair potentials (namely those which can be written as the sum of a non-negative potential plus an absolutely integrable and stable potential) combined with a method developed by Locatelli and Schoen (J. Glob. Optim. 2002) for establishing a lower bound for the minimal interatomic distance between particles interacting via a Morse potential in a cluster of minimum-energy configurations.