Geometrothermodynamic description of magnetic materials

TL;DR

This paper applies geometrothermodynamics to analyze three models of magnetic materials, revealing insights into their phase transitions and stability through curvature analysis, including a novel second-order transition in the spin model.

Contribution

It introduces a geometrothermodynamic framework for magnetic materials and uncovers a new second-order phase transition in the spin model.

Findings

Curvature analysis describes thermodynamic interactions and phase transitions.

Reproduces known behavior near the Curie temperature.

Identifies a new second-order phase transition in the spin model.

Abstract

We perform a statistical and geometrothermodynamic analysis of three different models of magnetic materials, namely, the translational free model, the spin model, and the mean-field model. First, we derive the fundamental equation for each model, which is then used as input to compute the metrics of the corresponding equilibrium spaces. Analyzing the corresponding geometrothermodynamic curvatures, we conclude that they can be used to describe thermodynamic interaction, stability conditions, and the phase transition structure of the modeled substances. In all the cases, we reproduce their well-known behavior close to the Curie temperature. Moreover, in the case of the model with spin, we found a curvature singularity which corresponds to a novel transition, where a particular response function diverges, indicating the presence of a second order phase transition, according to Ehrenfest classification.