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Journal of Experimental and Theoretical Physics

Phase transition properties of three-dimensional systems described by diluted potts model

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

Published Sep 1, 2009• 14 citations
Publisher

Abstract

Monte Carlo simulations are performed to analyze phase transitions in three-dimensional systems described by the 3-state Potts model with nonmagnetic impurities. Numerical results are presented for systems with spin concentrations p = 1.00, 0.95, 0.90, 0.80, 0.70, and 0.65 on lattices of size L varying between 20 and 44. Binder’s cumulant analysis shows that the introduction of quenched disorder in the form of non-magnetic impurities induces a crossover from first-order to second-order phase transition. The finite-size scaling method is used to calculate the static critical exponents α, γ, β, and ν for specific heat, susceptibility, magnetization, and correlation length, respectively.

DOI
10.1134/s1063776109090088

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Monte Carlo simulations are performed to analyze phase transitions in three-dimensional systems described by the 3-state Potts model with nonmagnetic impurities. Numerical results are presented for systems with spin concentrations p = 1.00, 0.95, 0.90, 0.80, 0.70, and 0.65 on lattices of size L varying between 20 and 44. Binder’s cumulant analysis shows that the introduction of quenched disorder in the form of non-magnetic impurities induces a crossover from first-order to second-order phase transition. The finite-size scaling method is used to calculate the static critical exponents α, γ, β, and ν for specific heat, susceptibility, magnetization, and correlation length, respectively.
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.
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 phase transitions and critical phenomena in three-dimensional (3D) site-diluted 3-and 4-state Potts models is investigated by Monte-Carlo method based on the highly efficient Wolff algorithm. The systems with linear sizesL=20-44 at spin concentrationsp=1.00, 0.95, 0.90, 0.80, 0.70, 0.65 are explored. The second-order phase transition is shown to occur in the three-dimensional 3-state Potts model with nonmagnetic impurities. In the 4-state Potts model there are observed first-order phase transitions in weakly diluted state, when the model is strongly diluted the first-order phase transitions change to the second-order one. On the basis of the finite-size scaling theory static critical exponents of specific heatα, susceptibilityγ, magnetizationβ, and exponent of correlation radiusνfor the systems under study are calculated.
The problem of the type of the phase transition in the three-dimensional weakly diluted Potts model with the number of spin states q = 3 has been investigated by the Monte Carlo method. The temperature dependences of the Binder cumulants, energy, magnetization, specific heat, and susceptibility have been calculated. It is found that the second-order phase transition occurs in a system at the spin concentration p = 0.9. The critical exponents of the magnetization (β), specific heat (α), and susceptibility (γ) and the critical correlation-length exponent v were calculated on the basis of the finite-size scaling theory at p = 0.9.