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Murtazaev A.K.,Russian Academy of Sciences | Ramazanov M.K.,Dagestan State Pedagogical University
Physics of the Solid State | Year: 2011

The replica Monte Carlo method has been applied to study critical properties of the three-dimensional frustrated antiferromagnetic Heisenberg model on a layered triangular lattice. Magnetic and chiral critical exponents for this model have been calculated within the finite-size scaling theory. The data for this model have been analyzed for the first time taking into account corrections to scaling. It has been shown that the critical behavior of the frustrated antiferromagnetic Heisenberg model on the triangular lattice differs from the critical behavior of the pure Heisenberg model and is independent of the type of interlayer exchange interaction. © 2011 Pleiades Publishing, Ltd.


Murtazaev A.K.,Russian Academy of Sciences | Babaev A.B.,Dagestan State Pedagogical University
Journal of Experimental and Theoretical Physics | Year: 2012

The phase transitions in the two-dimensional ferro- and antiferromagnetic Potts models with q = 3 states of spin on a triangular lattice are studied using cluster algorithms and the classical Monte Carlo method. Systems with linear sizes L = 20-120 are considered. The method of fourth-order Binder cumulants and histogram analysis are used to discover that a second-order phase transition occurs in the ferromagnetic Potts model and a first-order phase transition takes place in the antiferromagnetic Potts model. The static critical indices of heat capacity (α), magnetic susceptibility (γ), magnetization (β), and correlation radius index (ν) are calculated for the ferromagnetic Potts model using the finite-size scaling theory. © 2012 Pleiades Publishing, Ltd.


Murtazaev A.K.,Russian Academy of Sciences | Babaev A.B.,Dagestan State Pedagogical University
JETP Letters | Year: 2014

The effect of quenched nonmagnetic impurities on the phase transitions in the three-dimensional Potts model with the number of spin states q = 4 for the case of the simple cubic lattice is studied using the Monte Carlo method. The phase transitions in this model are studied for spin density p ranging from 1.0 to 0.70. The position of the tricritical point at the phase diagram is determined. © 2014, Maik Nauka-Interperiodica Publishing. All rights reserved.


Murtazaev A.K.,Russian Academy of Sciences | Babaev A.B.,Dagestan State Pedagogical University
Bulletin of the Russian Academy of Sciences: Physics | Year: 2014

The phase transitions in 2D ferro- and antiferromagnetic Potts models with number of spin states q = 3 on a triangular lattice are investigated by the cluster and classical Monte Carlo methods. Systems with linear sizes L = 20-120 are considered. Fourth-order Binder cumulants and histogram data analysis are used to show that second- and first-order phase transitions are observed in the ferromagnetic and antiferromagnetic Potts models, respectively. The static critical indices are calculated for specific heat α, susceptibility γ, magnetization β, and correlation length ν on the basis of finite-size scaling theory for a ferromagnetic Potts model. © 2014 Allerton Press, Inc.


Murtazaev A.K.,Russian Academy of Sciences | Babaev A.B.,Dagestan State Pedagogical University
Journal of Experimental and Theoretical Physics | Year: 2013

On the basis of a histogram data analysis, phase transitions (PTs) in a three-dimensional diluted ferromagnetic 3- and 4-state Potts models are investigated. Systems with linear dimensions of L = 20-60 and spin concentrations of p = 1.00, 0.95, and 0.65 are studied. It is shown that the introduction of weak disorder (p ∼ 0.95) into the system in the three-dimensional Potts model with q = 3 is sufficient to change a first-order phase transition to a second-order one, whereas, in the three-dimensional Potts model with q = 4, the change of a first-order phase transition to a second-order one occurs only in the presence of strong disorder (p ∼ 0.65). © 2013 Pleiades Publishing, Ltd.

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