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Journal of Surface Investigation X-ray Synchrotron and Neutron Techniques

Computer Simulation of the Phase Transitions in Three-Dimensional Weakly Diluted Spin Systems

Akai Kurbanovich Murtazaev, Albert Babaevich Babaev

Published Apr 1, 2022• 0 citations
Publisher

Abstract

Abstract A computer simulation of the phase transitions in a three-dimensional weakly diluted five-state Potts model on a simple cubic lattice is performed. Calculations are carried out for spin systems with periodic boundary conditions at spin concentrations of p = 1.0 and p = 0.90. Systems with linear dimensions L × L × L = N, L = 10–80 are considered. The temperature dependences of the specific heat, susceptibility, and magnetization as a function of the linear dimensions of the studied systems are obtained. Using the fourth-order Binder cumulants and using histogram-data analysis, it is shown that the presence of weak disorder in the form of nonmagnetic impurities of the order c = 10% (c = 1 – p, p is the spin concentration) does not affect the phase transition of the first-order.

DOI
10.1134/s1027451022030156

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Abstract A computer simulation of the phase transitions in a three-dimensional weakly diluted five-state Potts model on a simple cubic lattice is performed. Calculations are carried out for spin systems with periodic boundary conditions at spin concentrations of p = 1.0 and p = 0.90. Systems with linear dimensions L × L × L = N, L = 10–80 are considered. The temperature dependences of the specific heat, susceptibility, and magnetization as a function of the linear dimensions of the studied systems are obtained. Using the fourth-order Binder cumulants and using histogram-data analysis, it is shown that the presence of weak disorder in the form of nonmagnetic impurities of the order c = 10% (c = 1 – p, p is the spin concentration) does not affect the phase transition of the first-order.
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.
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.
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.
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 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.