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The Physics of Metals and Metallography

Calculating the Relative Variances of Magnetization, Heat Capacity, and Susceptibility in a Two-Dimensional Weakly Diluted Four-Component Potts Model

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

Published Jul 1, 2023• 0 citations
Publisher

Abstract

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.

DOI
10.1134/s0031918x2360094x

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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.
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.
Computer modelling of phase transitions in the four-component Potts model on a hexagonal lattice in pure and weakly diluted modes has been carried out. It is revealed that phase transitions of the second order are observed in the considered Potts models. The values of relative dispersions of magnetisation 𝑅𝑚, heat capacity and susceptibility are calculated. It is shown that for low-dimensional spin systems the values of the relativedispersions 𝑅𝑚, 𝑅𝑐, are different from zero at = and their decrease is observed at linear dimensions > 15.