  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.
