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Bulletin of the Russian Academy of Sciences Physics

Phase transitions in the two-dimensional antiferromagnetic Potts model on a triangular lattice

Akai Kurbanovich Murtazaev, Albert Babaevich Babaev

Published Oct 1, 2013• 5 citations
Publisher

Abstract

Phase transitions and thermodynamic properties in the two-dimensional three-state antiferromagnetic Potts model on a triangular lattice are investigated using the Monte Carlo method and the histogram analysis of the data. It is shown that pronounced first-order phase transitions are observed in this model for systems with rather large linear dimensions ( L > 120). No first-order PTs are observed for systems with L < 120.

DOI
10.3103/s1062873813100237

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Phase transitions and thermodynamic properties in the two-dimensional three-state antiferromagnetic Potts model on a triangular lattice are investigated using the Monte Carlo method and the histogram analysis of the data. It is shown that pronounced first-order phase transitions are observed in this model for systems with rather large linear dimensions ( L > 120). No first-order PTs are observed for systems with L < 120.
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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.
The thermodynamic properties and phase transitions in a two-dimensional strongly diluted threevertex antiferromagnetic Potts model on a triangular lattice have been investigated using the Monte Carlo method. The systems with linear dimensions of L × L = N , where L = 18–48, have been considered. It has been shown using the method of fourth-order Binder cumulants that, upon the introduction of nonmagnetic impurities into the spin system described by the two-dimensional antiferromagnetic Potts model, the firstorder phase transition changes to a second-order phase transition.
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.