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Physics of the Solid State

Phase Transitions in the Diluted Two-Dimensional Potts Model with the Number of Spin States q = 3 on a Square Lattice

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

Published May 1, 2022• 3 citations
Publisher

Abstract

Abstract The phase transitions in the two-dimensional diluted Potts model with the number of spin states q = 3 are studied by computer simulation method. The systems with linear sizes L × L = N, L = 10–160 at spin concentrations p = 1.00, 0.80 are considered. The obtained numerical data show that the second-order phase transition takes place in the pure Potts model with the number of spin states q = 3, according to the theory. The introduction of a disorder in the form of nonmagnetic impurities (p = 0.80) in the Potts model with q = 3 conserves the second-order phase transition.

DOI
10.1134/s1063783422060051

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Abstract The phase transitions in the two-dimensional diluted Potts model with the number of spin states q = 3 are studied by computer simulation method. The systems with linear sizes L × L = N, L = 10–160 at spin concentrations p = 1.00, 0.80 are considered. The obtained numerical data show that the second-order phase transition takes place in the pure Potts model with the number of spin states q = 3, according to the theory. The introduction of a disorder in the form of nonmagnetic impurities (p = 0.80) in the Potts model with q = 3 conserves the second-order phase transition.
The computer simulation method was used to study phase transitions in a two-dimensional site-diluted 3-state Potts model. Systems with linear dimensions Lx L=N, L=10/160 at a spin concentration p=1.00, 0.80 are considered. The numerical data obtained indicate that in a pure 3-state Potts model on a square lattice, a phase transition of the second order is observed in accordance with the theory. The introduction of disorder in the form of non-magnetic impurities (p=0.80) in the 3-state Potts model preserves the phase transition of the second order. Keywords: Potts model, Monte Carlo method, thermodynamic parameters, disorder.
Abstract Phase transitions in the two-dimensional slightly diluted Potts model on a square lattice at q = 5 have been studied using the computer simulation method. The systems with linear sizes L × L = N, L = 10–120 are considered. It is shown based on the forth-order Binder cumulants and using the histogram analysis of the data that the introduction of nonmagnetic impurities to a spin system described by the two-dimensional Potts model with q = 5 leads to a change of the first-order phase transition to a second-order phase transition.
Abstract Phase transitions and critical behavior in the 2D dilute Potts model with number q = 4 of spin states on a square lattice are investigated by computer simulation. Systems with linear sizes L × L = N, l = 10–160 with spin concentrations p = 1.00, 0.95, 0.80 are considered. It is shown that the introduction of magnetic impurities plays a stabilizing role in the realization of a second-order phase transition in the Potts model under investigation. Based on the finite-size scaling theory, statistical critical indices of heat capacity α, susceptibility γ, magnetization β, and correlation radius index ν are calculated for the range of concentrations p considered here.
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.
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.
The results of computer simulations of the critical behavior of three-dimensional structures described by disordered Potts models with q = 3 and q = 4 spin states are discussed. Systems with linear dimensions L = 20–60 with spin concentrations p = 1.00, 0.95, 0.90, 0.80, 0.70, and 0.65 are examined. It is found that in a three-dimensional Potts model with q = 3 spin states, introducing nonmagnetic impurities induces a second order phase transition. In a Potts model with q = 4, on the other hand, a shift from a first order phase transition to a second order phase transition is observed at high dilution (p = 0.65). Numerical values of the critical parameters are found using finite-size scaling theory and it is shown that they form a universality class corresponding to disordered systems.