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

Massimo Ostilli and Farrukh Mukhamedov

Physica A: Statistical Mechanics and its Applications, 2020, vol. 555, issue C

Abstract: We analyze a three-state Potts model built over a lattice ring, with coupling J0, 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 J0 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 (J0=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 J0 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 J0, 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 J0→−∞.

Keywords: Exact results; Potts model; Phase transitions; Effective mean field (search for similar items in EconPapers)
Date: 2020
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Persistent link: https://EconPapers.repec.org/RePEc:eee:phsmap:v:555:y:2020:i:c:s0378437120301631

DOI: 10.1016/j.physa.2020.124415

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