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Physics of the Solid State

Критическая температура трехвершинной модели Поттса на решетке Кагоме

А. Б. Бабаев, А.К. Муртазаев

Published Jan 1, 2019• 0 citations
Publisher

Abstract

The Potts model on the Kagome lattice is considered. The Monte Carlo method is used to obtain the temperature dependences of the thermodynamic parameters of heat capacity C, order parameter m, and susceptibility χ. The calculations were performed for systems with periodic boundary conditions. Systems with linear dimensions LxL = N, L = 20-90 were considered. Based on the fourth order Binder cumulant method, the critical temperature (Tc) was calculated for the three-vertex Potts model on the Kagome lattice. It is shown that the obtained Tc value within the statistical error is in good agreement with the results obtained using the transfer-matrix and polynomial approximation methods.

DOI
10.21883/ftt.2019.07.47848.400

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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.