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

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.

arXiv comment5 pages, 4 figures

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Cited by in corpus (5)

• Clock model interpolation and symmetry breaking in O(2) models
• Variational corner transfer matrix renormalization group method for classical statistical models
• Universal scaling of Klein bottle entropy near conformal critical points
• Extracting the Luttinger parameter from a single wave function
• Exploring quantum phase transitions by the cross derivative of the ground state energy