1D Three-state mean-field Potts model with first- and second-order phase transitions

摘要

We analyze a three-state Potts model built over a lattice ring, with coupling J(0), and the fully connected graph, with coupling J. This model is effectively mean-field and can be exactly solved by using transfer-matrix method and Cardano formula. When J and J(0) are both ferromagnetic, the model has a first-order phase transition which turns out to be a smooth modification of the known phase transition of the traditional meanfield Potts model (J(0) = 0), despite, as we prove, the connected correlation functions are now non zero, even in the paramagnetic phase. Furthermore, besides the first-order transition, there exists also a hidden continuous transition at a temperature below which the symmetric metastable state ceases to exist. When J is ferromagnetic and J(0) antiferromagnetic, a similar antiferromagnetic counterpart phase transition scenario applies. Quite interestingly, differently from the Ising-like two-state case, for large values of the antiferromagnetic coupling J(0), the critical temperature of the system tends to a finite value. Similarly, also the latent heat per spin tends to a finite constant in the limit of J(0) -> -infinity. (C) 2020 Elsevier B.V. All rights reserved.