On stable pair potentials with an attractive tail, remarks on two papers by A. G. Basuev

TL;DR

This paper revisits foundational work by Basuev to significantly improve the lower bounds on the convergence radius of the Mayer series for a broad class of stable, tempered potentials, including Lennard-Jones interactions.

Contribution

It demonstrates that Basuev's old results can be used to substantially enhance the known bounds on the convergence radius for Lennard-Jones and similar potentials.

Findings

Improved lower bound for Lennard-Jones gas convergence radius by a factor of 10^5.

Extended the applicability of Basuev's results to a large class of stable and tempered potentials.

Provided new insights into the convergence properties of the Mayer series for particle systems.

Abstract

We revisit two old and apparently little known papers by Basuev [2] [3] and show that the results contained there yield strong improvements on current lower bounds of the convergence radius of the Mayer series for continuous particle systems interacting via a very large class of stable and tempered potentials which includes the Lennard-Jones type potentials. In particular we analyze the case of the classical Lennard-Jones gas under the light of the Basuev scheme and, using also some new results [33] on this model recently obtained by one of us, we provide a new lower bound for the Mayer series convergence radius of the classical Lennard-Jones gas which improves by a factor of the order $10^5$ on the current best lower bound recently obtained in [17].