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Physics of the Solid State

Effect of quenched-in nonmagnetic impurities on phase transitions in a two-dimensional antiferromagnetic three-vertex Potts model on a triangular lattice

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

Published Jul 1, 2015• 8 citations
Publisher

Abstract

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.

DOI
10.1134/s1063783415070239

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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.
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.
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.
Abstract The influence of a weak disorder in the form of quenched nonmagnetic impurities on the phase transitions (PTs) in a three-dimensional 5-state Potts model is studied using the cluster Wolff algorithm of the Monte Carlo method. Systems with linear sizes L = 10–120 at spin concentrations p = 1.00 and 0.80 are considered. Using the fourth-order Binder cumulant method and histogram analysis, we show that the introduction of a weak quenched disorder (p = 0.80) in the form of nonmagnetic impurities changes a first-order PT into a second-order PT.
The Wolff cluster Monte Carlo algorithm is used to investigate the effect of frozen nonmagnetic canonically distributed impurities on the phase transitions in a two-dimensional Potts model with the spin state q = 5. Systems with linear dimensions L = 20–160 at spin concentrations p = 1.0 and 0.9 are considered. Using the fourth-order Binder cumulant method and the histogram analysis method it is shown that if a weak quenched disorder in the form of non-magnetic impurities (p = 0.9) is introduced in the system, the first-order phase transition changes to a second-order phase transition.
The influence of quenched nonmagnetic impurities on phase transitions and critical phenomena in the 3D Potts model with the spin state number q = 4 is studied using the Monte Carlo method. Systems with the linear size L = 20–32 and spin concentrations p = 1.00, 0.90, 0.65 are considered. The fourth order Binder cumulant method is used to demonstrate that in the strongly diluted regime, a phase transition of the second kind is observed in this model for the spin concentration p = 0.65, and a phase transition of the first kind is observed for the pure ( p = 1.00) and weakly diluted ( p = 0.90) models. The theory of finite-dimensional scaling is used to calculate the static critical parameters of heat capacity α, susceptibility γ, magnetization β, and correlation radius ν.
Abstract The effect of quenched non-magnetic impurities on phase transitions in low-dimensional Potts model structures is investigated by the Monte Carlo method using a cluster algorithm. Systems with linear dimensions of L = 20–160 and spin concentrations of p = 1.0, 0.9 are considered. Using the fourth-order Binder cumulant method and the histogram-data analysis method, the introduction of weak quenched disorder (p = 0.9) in the form of non-magnetic impurities is shown to change the order of the phase transition from the first to the second.