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Physics of the Solid State

Investigation of the thermodynamic properties and phase transitions in a strongly diluted three-vertex antiferromagnetic Potts model by the Monte Carlo method

Akai Kurbanovich Murtazaev, Albert Babaevich Babaev, G. Ya. Ataeva

Published Jan 1, 2017• 6 citations
Publisher

Abstract

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.

DOI
10.1134/s1063783417010231

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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 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.
Abstract The thermodynamic properties and phase transitions in the two-dimensional weakly diluted Potts model with the number of spin states q=4 were studied by the Monte Carlo method. Systems with linear dimensions L×L = N, L=10–160 are considered. Using the fourth order Binder cumulant method, critical temperatures were calculated for spin systems with a spin concentration p=1.0 and 0.90. Critical indices are calculated on the basis of the theory of finite-size scaling. The universality of the critical behavior of two-dimensional disordered systems is discussed.
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.
A Monte–Carlo method is used to study phase transitions and critical phenomena in a three-dimensional Potts model with 4 spin states and nonmagnetic impurities. Systems with linear sizes L=20–32 and spin concentrations p=1.00, 0.90, and 0.65 are studied. A fourth order Binder cumulant method is used to show that this model yields a second order phase transition for strong dilution with a spin concentration p=0.65, while the pure model (p=1.00) and the model with weak dilution (p=0.90) yield a first order phase transition. The static critical indices for the heat capacity α, susceptibility γ, magnetization β, and correlation radius ν are calculated using a finite-dimensional scaling theory.
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.
An influence of quenched nonmagnetic disorder on the phase transitions in the two dimensional antiferromagnetic Potts model with a number of spin state q=3 on a triangular lattice is calculated by the Monte-Carlo method. The systems with linear sizes L=20÷144 at spin concentrations p=1.00, 0.90, 0.80 are studied. By means of the fourth order Binder cumulant method, the inclusion of a quenched disorder as nonmagnetic impurities into a pure antiferromagnetic Potts model is shown to be the cause of the change of the first order phase transition into the second one.