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Physics of the Solid State

Фазовые переходы в двумерной слабо разбавленной пятивершинной модели Поттса

А.К. Муртазаев, А. Б. Бабаев, G. Ya. Ataeva

Published Jan 1, 2020• 0 citations
Publisher

Abstract

Computer simulation was used to study phase transitions in the two-dimensional weakly diluted Potts model on a square lattice at q=5. Systems with linear dimensions L×L=N, L=10-120 are considered. Based on fourth-order Binder cumulants, it was shown that the introduction of nonmagnetic impurities into the spin system described by the two-dimensional Potts model with q=5 leads to a change in the first-order phase transition to the second-order phase transition.

DOI
10.21883/ftt.2020.07.49478.051

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Computer simulation was used to study phase transitions in the two-dimensional weakly diluted Potts model on a square lattice at q=5. Systems with linear dimensions L×L=N, L=10-120 are considered. Based on fourth-order Binder cumulants, it was shown that the introduction of nonmagnetic impurities into the spin system described by the two-dimensional Potts model with q=5 leads to a change in the first-order phase transition to the second-order phase transition.
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 non-magnetic impurities has a stabilizing role in the implementation of the second-order phase transition in the Potts model under study on a hexagonal lattice.
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.
Abstract Phase transitions in the two-dimensional slightly diluted Potts model on a square lattice at q = 5 have been studied using the computer simulation method. The systems with linear sizes L × L = N, L = 10–120 are considered. It is shown based on the forth-order Binder cumulants and using the histogram analysis of the data that the introduction of nonmagnetic impurities to a spin system described by the two-dimensional Potts model with q = 5 leads to a change of the first-order phase transition to a second-order phase transition.
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.