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Journal of Experimental and Theoretical Physics

Effect of Quenched Nonmagnetic Impurities on the Phase Transitions in a Three-Dimensional Potts Model

Akai Kurbanovich Murtazaev, Albert Babaevich Babaev

Published Jun 1, 2021• 3 citations
Publisher

Abstract

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.

DOI
10.1134/s1063776121060054

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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.
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.
The influence of quenched nonmagnetic impurities on phase transitions in the three-dimensional Potts model with the number of spin states q = 3 is investigated using the Wolff single-cluster algorithm of the Monte Carlo method. The systems with linear sizes L = 20–44 at the spin concentrations p = 1.0, 0.9, 0.8, and 0.7 are analyzed. It is demonstrated with the use of the method of fourth-order Binder cumulants that the second-order phase transition occurs in the model under consideration at the spin concentrations p = 0.9, 0.8, and 0.7 and that the first-order phase transition is observed in the pure model ( p = 1.0). The static critical exponents α (heat capacity), γ (susceptibility), β (magnetization), and ν (correlation length) are calculated in the framework of the finite-size scaling theory. The problem regarding the universality classes of the critical behavior of weakly diluted systems is discussed.
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 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.
The effect of frozen disorder, implemented in the form of nonmagnetic impurities, on phase transitions in the three-dimensional Potts model with number of states q = 3 has was investigated by the Monte Carlo method, using the Wolf single-cluster algorithm. Systems with linear sizes L = 20–44 were considered at spin concentrations p = 1.00–0.65. The method of fourth-order Binder cumulants was used to demonstrate that a first-order phase transition is observed for the pure model ( p = 1.00) and a second-order phase transition occurs at concentrations p = 0.90, 0.80, 0.70, and 0.65.