Entropy-induced phase transitions in a hidden Potts model

A hidden state in which a spin does not interact with any other spin contributes to the entropy of an interacting spin system. We explore the q-state Potts model with extra r hidden states using the Ginzburg-Landau formalism in the mean-field limit. We analytically demonstrate that when 1<q≤2, the model exhibits a rich phase diagram comprising a variety of phase transitions such as continuous, discontinuous, two types of successive, and hybrid transitions; moreover, several characteristics such as critical point, critical endpoint, and tricritical point are identified. The critical line and critical endline merge in a singular form at the tricritical point. That supercritical behavior emerging at the tricritical point is, to the best our knowledge, novel. We microscopically investigate the origin of the discontinuous transition; it is induced by the competition between the interaction and entropy of the system in the Ising limit, whereas by the bistability of the hidden spin states in the percolation limit. Finally, we discuss the similarity and difference of the phase diagram generated in two types of Ising spins model.