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Journal of Experimental and Theoretical Physics

Phase Transitions in Two-Dimensional Potts Models on the Hexagonal Lattice

Akai Kurbanovich Murtazaev, Albert Babaevich Babaev

Published Jun 1, 2022• 5 citations
Publisher

Abstract

Abstract Phase transitions in 2D Potts models with the number of spin states q = 4 and 5 have been studied by computer simulation. Systems with linear sizes L = 21–180 have been considered. As follows from numerical data, the 2D Potts model on the hexagonal lattice demonstrates a first-order phase transition for the number of spin states q = 5 and a second-order phase transition for q = 4.

DOI
10.1134/s1063776122060036

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The Monte Carlo method is used to study phase transitions in the two-dimensional Potts model with the number of states spin q = 3 on square and hexagonal lattices. Considered systems with linear dimensions L × L = N, L = 21 ÷ 102. The obtained numerical data indicate that in the considered In the Potts model, a second-order phase transition is observed in accordance with the analytical theory. The Binder cumulants method of the fourth order determines the values ​​of the critical points of the Potts model on different lattices.

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Abstract Phase transitions in 2D Potts models with the number of spin states q = 4 and 5 have been studied by computer simulation. Systems with linear sizes L = 21–180 have been considered. As follows from numerical data, the 2D Potts model on the hexagonal lattice demonstrates a first-order phase transition for the number of spin states q = 5 and a second-order phase transition for q = 4.
The Monte Carlo method is used to study phase transitions in the two-dimensional Potts model with the number of states spin q=3 on square and hexagonal lattices. Considered systems with linear dimensions Lx L=N, L=21/102. The obtained numerical data indicate that in the considered In the Potts model, a second-order phase transition is observed in accordance with the analytical theory. The Binder cumulants method of the fourth order determines the values of the critical points of the Potts model on different lattices. Keywords: Phase transitions, Potts model, Monte Carlo, thermodynamic parameters, critical temperature.
Abstract The phase transitions in the two-dimensional diluted Potts model with the number of spin states q = 3 are studied by computer simulation method. The systems with linear sizes L × L = N, L = 10–160 at spin concentrations p = 1.00, 0.80 are considered. The obtained numerical data show that the second-order phase transition takes place in the pure Potts model with the number of spin states q = 3, according to the theory. The introduction of a disorder in the form of nonmagnetic impurities (p = 0.80) in the Potts model with q = 3 conserves the second-order phase transition.
Abstract Phase transitions in the two-dimensional slightly diluted Potts model on a square lattice at q = 5 have been studied using the computer simulation method. The systems with linear sizes L × L = N, L = 10–120 are considered. It is shown based on the forth-order Binder cumulants and using the histogram analysis of the data that the introduction of nonmagnetic impurities to a spin system described by the two-dimensional Potts model with q = 5 leads to a change of the first-order phase transition to a second-order phase transition.
Abstract Phase transitions and critical behavior in the 2D dilute Potts model with number q = 4 of spin states on a square lattice are investigated by computer simulation. Systems with linear sizes L × L = N, l = 10–160 with spin concentrations p = 1.00, 0.95, 0.80 are considered. It is shown that the introduction of magnetic impurities plays a stabilizing role in the realization of a second-order phase transition in the Potts model under investigation. Based on the finite-size scaling theory, statistical critical indices of heat capacity α, susceptibility γ, magnetization β, and correlation radius index ν are calculated for the range of concentrations p considered here.
The Monte Carlo method is used to study phase transitions in the two-dimensional Potts model with the number of states spin q = 3 on square and hexagonal lattices. Considered systems with linear dimensions L × L = N, L = 21 ÷ 102. The obtained numerical data indicate that in the considered In the Potts model, a second-order phase transition is observed in accordance with the analytical theory. The Binder cumulants method of the fourth order determines the values ​​of the critical points of the Potts model on different lattices.