A convenient method to detect the phase transitions in classical spin models

With an auxiliary weak external magnetic field, we rekindle the fundamental thermodynamic function, Gibbs free energy F (T , h), to investigate the phase transitions of classic spin lattice models. The transition temperatures are precisely located, by calculating the second-order derivative of the free energy with respect to both the magnetic field and the temperature, which also indicates the nature of the phase transitions. The method is convenient and universal, as illustrated by the 5-state clock model, 2-dimensional and 3-dimensional Ising model, and the XY model, whether a transition is trivial or exotic with complex excitation(s).