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Bulletin of the Russian Academy of Sciences Physics

Features of the phase transitions in the three-dimensional diluted potts model with number of spin states q = 3

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

Published May 1, 2010• 1 citation
Publisher

Abstract

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.

DOI
10.3103/s1062873810050291

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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.
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.
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 quenched nonmagnetic impurities on phase transitions in the three-dimensional Potts model with the number of spin states q=3 is studied using the Wolff single-cluster algorithm of the Monte Carlo method. By the method of fourth-order Binder cumulants, it is demonstrated that the second-order phase transition occurs in the model under study at spin concentrations p=0.9, 0.8, 0.7, and 0.65, while the first-order phase transition is observed in the pure model (p=1.0). The static critical exponents (CEs) α (heat capacity), γ (susceptibility), β (magnetization), and ν (correlation length) are calculated based on the finite-size scaling theory.
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.
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 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.