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Low Temperature Physics

Calculation of relative dispersions of magnetization, susceptibility, and heat capacity in a two-dimensional weakly diluted Potts model based on computer simulation methods

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

Published Feb 1, 2021• 2 citations
Publisher

Abstract

The Monte Carlo method was used to calculate the relative dispersions of the magnetization Rm, susceptibility Rχ, and heat capacity RC for a weakly diluted impurity Potts model with the number of spin states q = 4. It is shown that the introduction of disorder in the form of nonmagnetic impurities into the two-dimensional Potts model with q = 4 on square lattice leads to nonzero values for Rm, Rχ, and RC at the critical point.

DOI
10.1063/10.0003172

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The Monte Carlo method was used to calculate the relative dispersions of the magnetization Rm, susceptibility Rχ, and heat capacity RC for a weakly diluted impurity Potts model with the number of spin states q = 4. It is shown that the introduction of disorder in the form of nonmagnetic impurities into the two-dimensional Potts model with q = 4 on square lattice leads to nonzero values for Rm, Rχ, and RC at the critical point.
The relative variances of the magnetization Rm, heat capacity Rc, and susceptibility Rχ are calculated by the Monte Carlo method in the spin lattice four-component weakly diluted Potts model on a square lattice at a spin density p = 0.80. It is shown that introducing a disorder in the form of nonmagnetic impurities into the 2D Potts model leads to nonzero values of Rm, Rc, and Rχ at the critical point. It has been found that these values decrease noticeably for systems with linear sizes L ≥ 120 interatomic distances.
Abstract The relative variances of the magnetization Rm, heat capacity Rc, and susceptibility Rχ are calculated by the Monte Carlo method in the spin lattice four-component weakly diluted Potts model on a square lattice at a spin density p = 0.80. It is shown that introducing a disorder in the form of nonmagnetic impurities into the 2D Potts model leads to nonzero values of Rm, Rc, and Rχ at the critical point. It has been found that these values decrease noticeably for systems with linear sizes L ≥ 120 interatomic distances.
Using the Monte Carlo method, the relative dispersions of magnetization Rm, heat capacity Rc and susceptibility Rchi are calculated for a weakly diluted three-component Potts model on a square lattice at a spin concentration p=0.90. It is revealed that the introduction of disorder in the form of non-magnetic impurities into the two-dimensional Potts model leads to non-zero values for Rm, Rc, and Rchi at the critical point. It is found that these values decrease markedly for systems with linear dimensions L>80.
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.
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.