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Low Temperature Physics

Effect of quenched non-magnetic impurities on phase transitions in a two-dimensional Potts model

Albert Babaevich Babaev, Akai Kurbanovich Murtazaev

Published Jul 1, 2020• 7 citations
Publisher

Abstract

The Wolff cluster Monte Carlo algorithm is used to investigate the effect of frozen nonmagnetic canonically distributed impurities on the phase transitions in a two-dimensional Potts model with the spin state q = 5. Systems with linear dimensions L = 20–160 at spin concentrations p = 1.0 and 0.9 are considered. Using the fourth-order Binder cumulant method and the histogram analysis method it is shown that if a weak quenched disorder in the form of non-magnetic impurities (p = 0.9) is introduced in the system, the first-order phase transition changes to a second-order phase transition.

DOI
10.1063/10.0001365

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The Wolff cluster Monte Carlo algorithm is used to investigate the effect of frozen nonmagnetic canonically distributed impurities on the phase transitions in a two-dimensional Potts model with the spin state q = 5. Systems with linear dimensions L = 20–160 at spin concentrations p = 1.0 and 0.9 are considered. Using the fourth-order Binder cumulant method and the histogram analysis method it is shown that if a weak quenched disorder in the form of non-magnetic impurities (p = 0.9) is introduced in the system, the first-order phase transition changes to a second-order phase transition.
Abstract The effect of quenched non-magnetic impurities on phase transitions in low-dimensional Potts model structures is investigated by the Monte Carlo method using a cluster algorithm. Systems with linear dimensions of L = 20–160 and spin concentrations of p = 1.0, 0.9 are considered. Using the fourth-order Binder cumulant method and the histogram-data analysis method, the introduction of weak quenched disorder (p = 0.9) in the form of non-magnetic impurities is shown to change the order of the phase transition from the first to the second.
Abstract The influence of a weak disorder in the form of quenched nonmagnetic impurities on the phase transitions (PTs) in a three-dimensional 5-state Potts model is studied using the cluster Wolff algorithm of the Monte Carlo method. Systems with linear sizes L = 10–120 at spin concentrations p = 1.00 and 0.80 are considered. Using the fourth-order Binder cumulant method and histogram analysis, we show that the introduction of a weak quenched disorder (p = 0.80) in the form of nonmagnetic impurities changes a first-order PT into a second-order PT.
The influence of quenched nonmagnetic impurities on phase transitions in the three-dimensional Potts model with the number of spin states q = 3 is investigated using the Wolff single-cluster algorithm of the Monte Carlo method. The systems with linear sizes L = 20–44 at the spin concentrations p = 1.0, 0.9, 0.8, and 0.7 are analyzed. It is demonstrated with the use of the method of fourth-order Binder cumulants that the second-order phase transition occurs in the model under consideration at the spin concentrations p = 0.9, 0.8, and 0.7 and that the first-order phase transition is observed in the pure model ( p = 1.0). The static critical exponents α (heat capacity), γ (susceptibility), β (magnetization), and ν (correlation length) are calculated in the framework of the finite-size scaling theory. The problem regarding the universality classes of the critical behavior of weakly diluted systems is discussed.
The effect of quenched-in nonmagnetic impurities on phase transitions in a two-dimensional diluted antiferromagnetic three-vertex Potts model on a triangular lattice has been investigated using the Monte Carlo method. The systems with linear dimensions L × L = N and L = 9–144 have been considered. It has been shown using the fourth-order Binder cumulant method that the introduction of a quenched-in disorder into a spin system described by the two-dimensional antiferromagnetic Potts model leads to a change from the first-order phase transition to the 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.
The effect of frozen disorder, implemented in the form of nonmagnetic impurities, on phase transitions in the three-dimensional Potts model with number of states q = 3 has was investigated by the Monte Carlo method, using the Wolf single-cluster algorithm. Systems with linear sizes L = 20–44 were considered at spin concentrations p = 1.00–0.65. The method of fourth-order Binder cumulants was used to demonstrate that a first-order phase transition is observed for the pure model ( p = 1.00) and a second-order phase transition occurs at concentrations p = 0.90, 0.80, 0.70, and 0.65.