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Physics of the Solid State

Thermodynamic and magnetic properties of a three-state Potts model on a triangular lattice with next-neighbor interactions

Albert Babaevich Babaev, T. R. Rizvanova, Akai Kurbanovich Murtazaev

Published Dec 1, 2017• 7 citations
Publisher

Abstract

Using Monte Carlo calculations, we study the thermodynamic and magnetic properties of 2D structures that can be described by a three-state Potts model on a triangular lattice with nearest- and secondnearest- neighbor interactions characterized by the coupling constants J 1 and J 2, respectively. Analyzing the thermodynamic parameters of heat capacity, the order parameter, the susceptibility, and fourth-order Binder cumulants, we show that the three-state Potts model with coupling constants J 1 > 0 and J 2 < 0 predicts a phase transition of the second kind for 0 ≤ |r| ≤ 1/3, where r = J 2/J 1.

DOI
10.1134/s106378341712006x

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Using Monte Carlo calculations, we study the thermodynamic and magnetic properties of 2D structures that can be described by a three-state Potts model on a triangular lattice with nearest- and secondnearest- neighbor interactions characterized by the coupling constants J 1 and J 2, respectively. Analyzing the thermodynamic parameters of heat capacity, the order parameter, the susceptibility, and fourth-order Binder cumulants, we show that the three-state Potts model with coupling constants J 1 > 0 and J 2 < 0 predicts a phase transition of the second kind for 0 ≤ |r| ≤ 1/3, where r = J 2/J 1.
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.
The phase transitions in 2D ferro- and antiferromagnetic Potts models with number of spin states q = 3 on a triangular lattice are investigated by the cluster and classical Monte Carlo methods. Systems with linear sizes L = 20–120 are considered. Fourth-order Binder cumulants and histogram data analysis are used to show that second- and first-order phase transitions are observed in the ferromagnetic and antiferromagnetic Potts models, respectively. The static critical indices are calculated for specific heat α, susceptibility γ, magnetization β, and correlation length ν on the basis of finite-size scaling theory for a ferromagnetic Potts model.
Abstract The magnetic structures of the ground state, phase transitions, and the thermodynamic properties of a two-dimensional ferromagnetic Potts model with the number of spin states q = 4 on a hexagonal lattice are studied using the Wang–Landau algorithm of the Monte Carlo method, taking into account the interactions of the nearest and the next-nearest neighbors. It is shown that the inclusion of the antiferromagnetic interactions of the next-nearest neighbors leads to the appearance of frustration and disturbance of magnetic ordering. The phase transition characters are analyzed using the method of fourth-order Binder cumulants and the histogram method. It is found that a first-order phase transition takes place in this model.
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.
Using the Monte Carlo method we investigate the phase transitions and thermodynamic properties of magnetic structures with noncollinear directions of magnetic moments corresponded to antiferromagnetic q=4 Potts model on a face-centered cubic lattice. Monte Carlo simulations are performed on lattices with linear sizes L=20÷44. Thermodynamic parameters: the order parameter mAF, susceptibility χ, internal energy U, and specific heat C are evaluated for all studied systems. By employing the fourth order Binder cumulant method, a first order transition is shown to be occurred in the model.
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.