Rigorous Proof of a Liquid-Vapor Phase Transition in a Continuum Particle System

TL;DR

This paper rigorously proves the existence of a liquid-vapor phase transition in a continuum particle system with long-range interactions, extending mean field theory results to finite but large interaction ranges.

Contribution

It provides a rigorous mathematical proof of a liquid-gas phase transition in a continuum particle system with finite but long interaction range, beyond mean field theory.

Findings

Existence of a liquid-gas phase transition for long but finite interaction ranges.

Extension of mean field theory to finite interaction ranges.

Mathematical proof applicable to particles in bbr^d, d bgeq 2.

Abstract

We consider particles in ${\Bbb R}^d, d \geq 2$, interacting via attractive pair and repulsive four-body potentials of the Kac type. Perturbing about mean field theory, valid when the interaction range becomes infinite, we prove rigorously the existence of a liquid-gas phase transition when the interaction range is finite but long compared to the interparticle spacing.