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Physics of the Solid State

Фазовые переходы в трехмерной слабо разбавленной модели Поттса с q=5

Akai Kurbanovich Murtazaev, Albert Babaevich Babaev

Published Jan 1, 2021• 1 citation
Publisher

Abstract

The study of phase transitions in a three-dimensional weakly diluted 5-state Potts model is carried out by computer modeling. Systems with linear sizes L × L × L = N, L = 10 ÷ 40 at a spin concentration p = 1.00, 0.90 are considered. The obtained numerical data indicate that the introduction of an insignificant disorder in the form of non-magnetic impurities (p = 0.90) in the three-dimensional 5 - state Potts model is not essential for a phase transition of the first order.

DOI
10.21883/ftt.2021.10.51417.047

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The study of phase transitions in a three-dimensional weakly diluted 5-state Potts model is carried out by computer modeling. Systems with linear sizes L × L × L = N, L = 10 ÷ 40 at a spin concentration p = 1.00, 0.90 are considered. The obtained numerical data indicate that the introduction of an insignificant disorder in the form of non-magnetic impurities (p = 0.90) in the three-dimensional 5 - state Potts model is not essential for a phase transition of the first order.
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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.
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.
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.