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Physics of the Solid State

Компьютерное моделирование критического поведения двумерной слаборазбавленной антиферромагнитной модели Поттса на треугольной решетке

А.Б. Бабаев, Akai Kurbanovich Murtazaev, G. Ya. Ataeva, T. R. Rizvanova, M.R. Dzhamaludinov

Published Jan 1, 2018• 0 citations
Publisher

Abstract

AbstractThe critical behavior of a two-dimensional weakly diluted antiferromagnetic Potts model with spin states q = 3 on a triangular lattice is computationally simulated. The systems with periodic boundary conditions were calculated, when spin concentrations p were 1.0 and 0.9. Systems with linear dimensions L × L = N and L = 9–144 were considered. Static critical exponents of heat capacity α, the susceptibility γ, the order parameter β, and critical exponent ν for a correlation radius are calculated based on a theory of finite-dimensional scaling.

DOI
10.21883/ftt.2018.06.45995.07m

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AbstractThe critical behavior of a two-dimensional weakly diluted antiferromagnetic Potts model with spin states q = 3 on a triangular lattice is computationally simulated. The systems with periodic boundary conditions were calculated, when spin concentrations p were 1.0 and 0.9. Systems with linear dimensions L × L = N and L = 9–144 were considered. Static critical exponents of heat capacity α, the susceptibility γ, the order parameter β, and critical exponent ν for a correlation radius are calculated based on a theory of finite-dimensional scaling.
The critical behavior of a two-dimensional weakly diluted antiferromagnetic Potts model with spin states q = 3 on a triangular lattice is computationally simulated. The systems with periodic boundary conditions were calculated, when spin concentrations p were 1.0 and 0.9. Systems with linear dimensions L × L = N and L = 9–144 were considered. Static critical exponents of heat capacity α, the susceptibility γ, the order parameter β, and critical exponent ν for a correlation radius are calculated based on a theory of finite-dimensional scaling.
A computer simulation of the critical behavior of a two-dimensional highly diluted 3-state antiferromagnetic Potts model on a triangular lattice is performed. The calculations are done for systems with periodic boundary conditions at spin concentrations p equal to 0.70 and 0.65. Systems with linear dimensions L×L = N, L = 20–144 are considered. Based on the theory of finite-dimensional scaling, the static critical exponents of heat capacity α, susceptibility γ, order parameter β, and critical index ν for the correlation radius are calculated. It is numerically shown that the calculated critical exponents vary with changes in the spin concentration p, while the ratios β/ν and γ/ν remain unchanged within error, showing a weak universality of the critical behavior of disordered systems.
By introducing a small amount of non-magnetic impurities into an antiferromagnetic (AF) two-dimensional (2D) Potts model on a triangular lattice it is that the impurities in spin systems described by this model result in the change of a first order to a second-order phase transition. The systems with linear sizes L × L = N, L = 9-144 are considered. Investigations are performed using the standard Metropolis algorithm along with Monte-Carlo single-cluster Wolff algorithm. On the basis of the theory of finite-size scaling, critical exponents (CE) are calculated: the heat capacity α, the susceptibility γ, the order parameter β, and the CE of the correlation radius ν.
The critical behavior of the disordered two-dimensional antiferromagnetic Potts model with the number of spin states q= 3 on a triangular lattice with disorder in the form of nonmagnetic impurities is studied by the Monte Carlo method. The critical exponents for the susceptibility γ, magnetization β, specific heat α, and correlation radius ν are calculated in the framework of the finite-size scaling theory at spin concentrations p = 0.90, 0.80, 0.70, and 0.65. It is found that the critical exponents increase with the degree of disorder, whereas the ratios and do not change, thus holding the scaling equality 2βν+γν=d\frac{{2\beta }}{\nu } + \frac{\gamma }{\nu } = dν2β​+νγ​=d . Such behavior of the critical exponents is related to the weak universality of the critical behavior characteristic of disordered systems. All results are obtained using independent Monte Carlo algorithms, such as the Metropolis and Wolff algorithms.