Cross derivative: a universal and efficient method for phase transitions in classical spin models

TL;DR

This paper introduces a universal and efficient method using a cross derivative of Gibbs free energy to accurately identify and characterize phase transitions in various classical spin models, including trivial and exotic types.

Contribution

The authors propose a novel cross derivative approach of Gibbs free energy that effectively detects phase transitions across multiple classical spin models, regardless of their complexity.

Findings

Accurately locates critical temperatures in diverse models.

Reveals the nature of phase transitions through the cross derivative.

Applicable to models with complex excitations and exotic transitions.

Abstract

With an auxiliary weak external magnetic field, we reexamine the fundamental thermodynamic function, Gibbs free energy F(T, h), to study the phase transitions in the classical spin lattice models. A cross derivative, i.e. the second-order partial derivative of F(T, h) with respect to both temperature and field, is calculated to precisely locate the critical temperature, which also reveals the nature of a transition. The strategy is efficient and universal, as exemplified by the 5-state clock model, 2-dimensional (2D) and 3D Ising models, and the XY model, no matter a transition is trivial or exotic with complex excitations. More importantly, other conjugate pairs could also be integrated into a similar cross derivative if necessary, which would greatly enrich our vision and means to investigate phase transitions both theoretically and experimentally.