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With an auxiliary weak external magnetic field, we reexamine the fundamentalthermodynamic function, Gibbs free energy F(T, h), to study the phasetransitions in the classical spin lattice models. A cross derivative, i.e. thesecond-order partial derivative of F(T, h) with respect to both temperature andfield, is calculated to precisely locate the critical temperature, which alsoreveals the nature of a transition. The strategy is efficient and universal, asexemplified 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 complexexcitations. More importantly, other conjugate pairs could also be integratedinto a similar cross derivative if necessary, which would greatly enrich ourvision and means to investigate phase transitions both theoretically andexperimentally.

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