Curie-Weiss magnet: a simple model of phase transition

TL;DR

The paper provides a detailed analysis of the Curie-Weiss model, an exactly solvable ferromagnetic system, highlighting its thermodynamic properties near the critical temperature and its significance in statistical mechanics and information theory.

Contribution

It offers a comprehensive discussion of the Curie-Weiss model, including exact, approximate, and numerical results, and derives the exact expression for the limiting magnetic field.

Findings

Exact expression for the limiting magnetic field

Properties of the model near the critical temperature

Comparison of exact, approximate, and numerical results

Abstract

The Curie-Weiss model is an exactly soluble model of ferromagnetism that allows one to study in detail the thermodynamic functions, in particular their properties in the neighbourhood of the critical temperature. In this model every magnetic moment interacts with every other magnetic moment. Because of its simplicity and because of the correctness of at least of some of its predictions, the Curie-Weiss model occupies an important place in the statistical mechanics literature and its application to information theory. It is frequently presented as an introduction to the Ising model or to spin glass models, and usually only general features of the Curie-Weiss model are presented. We discuss here properties of this model in a rather detailed way. We present the exact, approximate and numerical results for this particular model. The exact expression for the limiting magnetic field is derived.