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

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.

15 pages, 6 figures, 1 table

References in corpus (1)

• Continuous Spin Mean-Field models: Limiting kernels and Gibbs Properties of local transforms

Cited by in corpus (2)

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