## Abstract

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 mean-field 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}→−∞.

Original language | English |
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Article number | 124415 |

Journal | Physica A: Statistical Mechanics and its Applications |

Volume | 555 |

DOIs | |

Publication status | Published - Oct 1 2020 |

## Keywords

- Effective mean field
- Exact results
- Phase transitions
- Potts model

## ASJC Scopus subject areas

- Statistics and Probability
- Condensed Matter Physics