Generalized Gibbs Phase Rule and Multicriticality Applied to Magnetic Systems

A generalization of the original Gibbs phase rule is proposed in order to study the presence of single phases, multiphase coexistence, and multicritical phenomena in lattice spin magnetic models. The rule is based on counting the thermodynamic number of degrees of freedom, which strongly depends on the external fields needed to break the ground state degeneracy of the model. The phase diagrams of some spin Hamiltonians are analyzed according to this general phase rule, including general spin Ising and Blume-Capel models, as well as q-state Potts models. It is shown that by properly taking into account the intensive fields of the model in study, the generalized Gibbs phase rule furnishes a good description of the possible topology of the corresponding phase diagram. Although this scheme is unfortunately not able to locate the phase boundaries, it is quite useful to at least provide a good description regarding the possible presence of critical and multicritical surfaces, as well as isolated multicritical points.