Physics of the Solid State

Phase transitions in the diluted 2D three-state Potts model on a square lattice

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

Published Jan 1, 2022• 1 citation

Abstract

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.

DOI: 10.21883/pss.2022.06.53824.285

Related papers

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

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.

Physics of the Solid StateMay 1, 20223 citations

Computer simulation of phase transitions in low-dimensional Potts models

Akai Kurbanovich Murtazaev, Albert Babaevich Babaev, М. А. Магомедов

The Monte Carlo method is used to study phase transitions in the two-dimensional Potts model with the number of states spin q=3 on square and hexagonal lattices. Considered systems with linear dimensions Lx L=N, L=21/102. The obtained numerical data indicate that in the considered In the Potts model, a second-order phase transition is observed in accordance with the analytical theory. The Binder cumulants method of the fourth order determines the values of the critical points of the Potts model on different lattices. Keywords: Phase transitions, Potts model, Monte Carlo, thermodynamic parameters, critical temperature.

Physics of the Solid StateJan 1, 20220 citations

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

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

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.

Journal of Experimental and Theoretical PhysicsSep 1, 200914 citations

Phase Transitions and Critical Phenomena in the 2D Potts Impurity Model on a Square Lattice

Akai Kurbanovich Murtazaev, Albert Babaevich Babaev, G. Ya. Ataeva +1 more

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.

Journal of Experimental and Theoretical PhysicsSep 1, 20224 citations

Phase transitions in a two-dimensional weakly diluted 4-state Potts model on a hexagonal lattice

А. Б. Бабаев, Муртазаев А.К.

The Monte Carlo method is used to study phase transitions in a two-dimensional weakly diluted 4-state Potts model on a hexagonal lattice. Systems with linear dimensions L=21/336 at spin concentrations p=1.00, 0.90 are considered. The use of the fourth-order binder cumulants method and histogram data analysis showed that the introduction of nonmagnetic impurities has a stabilizing role in the implementation of the second-order phase transition in the Potts model under study on a hexagonal lattice. Keywords: Potts model, Monte Carlo method, thermodynamic parameters, disorder.

Physics of the Solid StateJan 1, 20230 citations

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

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.

Bulletin of the Russian Academy of Sciences PhysicsMay 1, 20101 citation