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.

5 pages, 4 figures

References in corpus (7)

• Classical simulation of infinite-size quantum lattice systems in one spatial dimension
• Phase transition of the q-state clock model: duality and tensor renormalization
• Non-Kosterlitz-Thouless transitions for the $q$-state clock models
• Phase Transitions of Ferromagnetic Potts Models on the Simple Cubic Lattice
• Direct Evidence of the Discontinuous Character of the Kosterlitz-Thouless Jump
• Universal entropy of conformal critical theories on a Klein bottle
• DMRG study of the Berezinskii-Kosterlitz-Thouless transitions of the 2D five-state clock model

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