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Physics of the Solid State

Phase Transitions in Low-Dimensional Disordered Potts Models

Albert Babaevich Babaev, Akai Kurbanovich Murtazaev

Published May 1, 2020• 7 citations
Publisher

Abstract

Abstract The Monte Carlo method is used to study phase transitions in disordered two-dimensional Potts models in which disorder is realized as nonmagnetic impurities. The temperature dependences of the thermodynamic parameters have been calculated for specific heat C, susceptibility χ, and fourth-order Binder cumulants in the dependence on spin concentration p. The calculations have been performed for the system with periodic boundary conditions. The systems with linear sizes L × L = N, L = 20–160 are considered. The incorporation of nonmagnetic impurities to a spin system is shown to possibly lead to a change of the first-order phase transition to a second-order phase transition. The problem of the universality classes of the critical behavior of low-dimensional diluted systems is discussed.

DOI
10.1134/s1063783420050042

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Abstract The Monte Carlo method is used to study phase transitions in disordered two-dimensional Potts models in which disorder is realized as nonmagnetic impurities. The temperature dependences of the thermodynamic parameters have been calculated for specific heat C, susceptibility χ, and fourth-order Binder cumulants in the dependence on spin concentration p. The calculations have been performed for the system with periodic boundary conditions. The systems with linear sizes L × L = N, L = 20–160 are considered. The incorporation of nonmagnetic impurities to a spin system is shown to possibly lead to a change of the first-order phase transition to a second-order phase transition. The problem of the universality classes of the critical behavior of low-dimensional diluted systems is discussed.
Abstract The Monte Carlo method is used to study phase transitions in disordered two-dimensional Potts models in which disorder is realized as nonmagnetic impurities. The temperature dependences of the thermodynamic parameters have been calculated for specific heat C , susceptibility χ, and fourth-order Binder cumulants in the dependence on spin concentration p . The calculations have been performed for the system with periodic boundary conditions. The systems with linear sizes L × L = N , L = 20–160 are considered. The incorporation of nonmagnetic impurities to a spin system is shown to possibly lead to a change of the first-order phase transition to a second-order phase transition. The problem of the universality classes of the critical behavior of low-dimensional diluted systems is discussed.
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 The phase transitions in the two-dimensional impurity Potts model on a square lattice are investigated on the basis of numerical methods of computational physics. The calculations are performed for weakly diluted systems with periodic boundary conditions at a spin concentration of p = 0.95. Systems with linear dimensions of L × L = N, L = 10–160 are considered. The effect of insignificant disorder in the form of quenched-in non-magnetic impurities on first-order phase transitions is studied. The temperature dependences of the heat capacity, susceptibility, and magnetization are given as functions of the linear dimensions of the systems under study. Using the fourth-order Binder cumulant method and histogram analysis of the data, it is shown that a small impurity concentration of c = 5% (c = 1 – p) is sufficient to change the order of the phase transition from the first to the second.
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 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.