A phase transition in a Curie-Weiss system with binary interactions

TL;DR

This paper investigates a continuum Curie-Weiss model with binary interactions, revealing a phase transition characterized by coexistence points and deriving an equation of state for the system.

Contribution

It introduces a novel continuum Curie-Weiss model with binary interactions and analyzes phase coexistence and the equation of state.

Findings

Existence of phase coexistence points in the model.

Derivation of an equation of state for the system.

Identification of phase transition behavior.

Abstract

A single-sort continuum Curie-Weiss system of interacting particles is studied. The particles are placed in the space $\mathbb{R}^d$ divided into congruent cubic cells. For a region $V\subset \mathbb{R}^d$ consisting of $N\in \mathbb{N}$ cells, every two particles contained in $V$ attract each other with intensity $J_1/N$. The particles contained in the same cell are subjected to binary repulsion with intensity $J_2>J_1$. For fixed values of the temperature, the interaction intensities, and the chemical potential the thermodynamic phase is defined as a probability measure on the space of occupation numbers of cells, determined by a condition typical of Curie-Weiss theories. It is proved that the half-plane $J_1\,\times\,$\textit{chemical potential} contains phase coexistence points at which there exist two thermodynamic phases of the system. An equation of state for this system is obtained.