A Curie-Weiss Theory of the Continuum Widom-Rowlinson Model

TL;DR

This paper introduces a continuum Widom-Rowlinson model with a novel multi-particle interaction, providing a rigorous theoretical framework for phase transitions in this two-component gas system.

Contribution

It develops a new continuum Widom-Rowlinson model and establishes a rigorous theory of phase transitions within the grand canonical formalism.

Findings

Thermodynamic equivalence to a one-component gas with multi-particle interaction

Rigorous proof of phase transition existence

Framework for constructing phase transitions in the model

Abstract

A version of the continuum Widom-Rowlinson model is introduced and studied. It is a two-component gas of point particles placed in $\mathbf{R}^d$ in which like particles do not interact and unlike particles contained in a given vessel of volume $V$ repel each other with intensity $a/V$. This model is thermodynamically equivalent to a one-component gas with multi-particle interaction. For both models, a rigorous theory of a phase transition is presented and the ways of its construction in the framework of the grand canonical formalism are outlined.