TY - JOUR

T1 - 1D Three-state mean-field Potts model with first- and second-order phase transitions

AU - Ostilli, Massimo

AU - Mukhamedov, Farrukh

N1 - Funding Information:
M. O. acknowledges Grant CNPq 09/2018 - PQ (Brazil). F. M. thanks UAEU UPAR Grant No. 31S391 .
Publisher Copyright:
© 2020 Elsevier B.V.

PY - 2020/10/1

Y1 - 2020/10/1

N2 - 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→−∞.

AB - 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→−∞.

KW - Effective mean field

KW - Exact results

KW - Phase transitions

KW - Potts model

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U2 - 10.1016/j.physa.2020.124415

DO - 10.1016/j.physa.2020.124415

M3 - Article

AN - SCOPUS:85081013664

SN - 0378-4371

VL - 555

JO - Physica A: Statistical Mechanics and its Applications

JF - Physica A: Statistical Mechanics and its Applications

M1 - 124415

ER -