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Physics of the Solid State

Phase Transitions and the Thermodynamic Properties of the Potts Model with the Number of Spin States q = 4 on a Triangular Lattice

Akai Kurbanovich Murtazaev, Djuma R. Kurbanova, Рамазанов Магомедшейх Курбанович

Published Nov 1, 2019• 9 citations
Publisher

Abstract

Abstract The phase transitions and the thermodynamic properties of the two-dimensional ferromagnetic Potts model with the number of spin states q = 4 on a triangular lattice are studied on the base of the Wang–Landau algorithm of the Monte Carlo method. The phase transition characters are analyzed using the method of the four-order Binder cumulants and the histogram analysis of the data. It is found that a first-order phase transition is observed in the model under study.

DOI
10.1134/s1063783419110234

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Abstract The phase transitions and the thermodynamic properties of the two-dimensional ferromagnetic Potts model with the number of spin states q = 4 on a triangular lattice are studied on the base of the Wang–Landau algorithm of the Monte Carlo method. The phase transition characters are analyzed using the method of the four-order Binder cumulants and the histogram analysis of the data. It is found that a first-order phase transition is observed in the model under study.
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The phase transitions in the two-dimensional ferro- and antiferromagnetic Potts models with q = 3 states of spin on a triangular lattice are studied using cluster algorithms and the classical Monte Carlo method. Systems with linear sizes L = 20–120 are considered. The method of fourth-order Binder cumulants and histogram analysis are used to discover that a second-order phase transition occurs in the ferromagnetic Potts model and a first-order phase transition takes place in the antiferromagnetic Potts model. The static critical indices of heat capacity (α), magnetic susceptibility (γ), magnetization (β), and correlation radius index (ν) are calculated for the ferromagnetic Potts model using the finite-size scaling theory.
Phase transitions in the two-dimensional ferromagnetic Potts model with the number of spin states q = 3 on a triangular lattice were studied using Monte-Carlo method. The systems of linear size L = 20–120 were considered. Using the method of the fourth-order Binder cumulants, it was demonstrated that the second order phase transition is observed in the two-dimensional ferromagnetic Potts model. The static critical exponents for the heat capacity α, susceptibility γ, magnetization β and correlation radius ν were calculated based on the finite-dimensional scaling theory.