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Bulletin of the Russian Academy of Sciences Physics

Phase Transitions in the Weakly Diluted 4-State Potts Model on a Triangular Lattice

Albert Babaevich Babaev, Akai Kurbanovich Murtazaev

Published Dec 1, 2024• 0 citations
Publisher

Abstract

Abstract We report a numerical study of the weakly diluted 4-state Potts model on a triangular lattice using Monte Carlo method. We consider systems with linear dimensions L × L = N, L = 10–160. Phase transitions in the Potts model are investigated employing the fourth-order Binder cumulants method and the histogram data analysis. Second-order phase transitions which are close to weakly first-order transitions are shown to occur in the 4-state Potts model on a triangular lattice. The addition of a nonmagnetic disorder has a stabilizing role in the realization of second-order phase transitions.

DOI
10.1134/s1062873824708699

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Abstract We report a numerical study of the weakly diluted 4-state Potts model on a triangular lattice using Monte Carlo method. We consider systems with linear dimensions L × L = N, L = 10–160. Phase transitions in the Potts model are investigated employing the fourth-order Binder cumulants method and the histogram data analysis. Second-order phase transitions which are close to weakly first-order transitions are shown to occur in the 4-state Potts model on a triangular lattice. The addition of a nonmagnetic disorder has a stabilizing role in the realization of second-order phase transitions.
The Monte Carlo method is used to study phase transitions in a two-dimensional weakly diluted 4-state Potts model on a hexagonal lattice. Systems with linear dimensions L=21/336 at spin concentrations p=1.00, 0.90 are considered. The use of the fourth-order binder cumulants method and histogram data analysis showed that the introduction of nonmagnetic impurities has a stabilizing role in the implementation of the second-order phase transition in the Potts model under study on a hexagonal lattice. Keywords: Potts model, Monte Carlo method, thermodynamic parameters, disorder.
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.
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 A computer simulation of the phase transitions in a three-dimensional weakly diluted five-state Potts model on a simple cubic lattice is performed. Calculations are carried out for spin systems with periodic boundary conditions at spin concentrations of p = 1.0 and p = 0.90. Systems with linear dimensions L × L × L = N, L = 10–80 are considered. The temperature dependences of the specific heat, susceptibility, and magnetization as a function of the linear dimensions of the studied systems are obtained. Using the fourth-order Binder cumulants and using histogram-data analysis, it is shown that the presence of weak disorder in the form of nonmagnetic impurities of the order c = 10% (c = 1 – p, p is the spin concentration) does not affect the phase transition of the first-order.
The effect of quenched-in nonmagnetic impurities on phase transitions in a two-dimensional diluted antiferromagnetic three-vertex Potts model on a triangular lattice has been investigated using the Monte Carlo method. The systems with linear dimensions L × L = N and L = 9–144 have been considered. It has been shown using the fourth-order Binder cumulant method that the introduction of a quenched-in disorder into a spin system described by the two-dimensional antiferromagnetic Potts model leads to a change from the first-order phase transition to the second-order phase transition.