Phase behavior of a cell model with Curie-Weiss interaction

TL;DR

This paper derives an explicit equation of state for a cell model with Curie-Weiss interaction, revealing a sequence of first-order phase transitions and providing a microscopic definition of the critical temperature.

Contribution

It introduces an explicit equation of state for the Curie-Weiss cell model and analyzes its phase transitions based on microscopic parameters.

Findings

Sequence of first-order phase transitions below critical temperature

Explicit phase diagrams for the first three transitions

Mathematically strict definition of critical temperature

Abstract

The object of this study is a cell model with Curie-Weiss interaction potential. We have already proved the possibility of a mathematically rigorous transition from a continuous system of interacting particles to such a model and made an accurate calculation of its grand partition function. In the present research, we derive an explicit accurate equation of state of the cell model with Curie-Weiss potential. It turned out that this model has a sequence of first-order phase transitions at temperatures below the critical. We analyzed the mechanism of these transitions based on the behavior of the chemical potential as a function of density. Thus we found the points of phase coexistence without going beyond the microscopic approach. We also proposed a mathematically strict definition of the critical temperature as a function of the microscopic parameters of the model. We determined the parameters of the critical points and plotted phase diagrams which cover the area of the first three phase transitions in the sequence.