Liquid-Vapor Phase Transitions for Systems with Finite Range Interactions

TL;DR

This paper rigorously proves the existence of liquid-gas phase transitions in systems with finite-range attractive and repulsive interactions, extending mean field theory to more realistic finite interaction ranges.

Contribution

It establishes the occurrence of phase transitions for particles with finite-range interactions, bridging the gap between mean field theory and realistic systems.

Findings

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

Extension of mean field results to finite-range interactions.

Rigorous mathematical proof of phase transition under specified conditions.

Abstract

We consider particles in $\R^d, d \geq 2$ 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 for a range of temperature.