Mayer and virial series at low temperature

TL;DR

This paper investigates the low-temperature behavior of Mayer and virial series in a classical particle system, providing physical interpretations of their convergence radii and implications for phase transitions.

Contribution

It offers novel physical insights into the convergence radii of Mayer and virial series at low temperature, independent of phase transition considerations.

Findings

Mayer radius indicates rapid density increase from very small to finite values.

Virial radius signifies a transition from monatomic to polyatomic gas.

Results align with Lee-Yang theorem and Widom-Rowlinson model predictions.

Abstract

We analyze the Mayer pressure-activity and virial pressure-density series for a classical system of particles in continuous configuration space at low temperature. Particles interact via a finite range potential with an attractive tail. We propose physical interpretations of the Mayer and virial series' radius of convergence, valid independently of the question of phase transition: the Mayer radius corresponds to a fast increase from very small to finite density, and the virial radius corresponds to a cross-over from monatomic to polyatomic gas. Our results have consequences for the search of a low density, low temperature solid-gas phase transition, consistent with the Lee-Yang theorem for lattice gases and with the continuum Widom-Rowlinson model.