Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

Physics of the Solid State

Phase Transitions in the Two-Dimensional Slightly Diluted Five-Vertex Potts Model

Akai Kurbanovich Murtazaev, Albert Babaevich Babaev, G. Ya. Ataeva

Published Jul 1, 2020• 3 citations
Publisher

Abstract

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.

DOI
10.1134/s1063783420070185

Related papers

Phase Transitions in Two-Dimensional Structures Described by Impurity Potts Models

Akai Kurbanovich Murtazaev, Albert Babaevich Babaev, G. Ya. Ataeva +1 more

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.

Journal of Surface Investigation X-ray Synchrotron and Neutron Techniques•Sep 1, 2021•0 citations

Фазовые переходы в двумерной слабо разбавленной пятивершинной модели Поттса

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

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.

Physics of the Solid State•Jan 1, 2020•0 citations

Effect of quenched-in nonmagnetic impurities on phase transitions in a two-dimensional antiferromagnetic three-vertex Potts model on a triangular lattice

Akai Kurbanovich Murtazaev, Albert Babaevich Babaev, G. Ya. Ataeva

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.

Physics of the Solid State•Jul 1, 2015•8 citations

Phase Transitions in the Diluted Two-Dimensional Potts Model with the Number of Spin States q = 3 on a Square Lattice

Akai Kurbanovich Murtazaev, Albert Babaevich Babaev, G. Ya. Ataeva

Abstract The phase transitions in the two-dimensional diluted Potts model with the number of spin states q = 3 are studied by computer simulation method. The systems with linear sizes L × L = N, L = 10–160 at spin concentrations p = 1.00, 0.80 are considered. The obtained numerical data show that the second-order phase transition takes place in the pure Potts model with the number of spin states q = 3, according to the theory. The introduction of a disorder in the form of nonmagnetic impurities (p = 0.80) in the Potts model with q = 3 conserves the second-order phase transition.

Physics of the Solid State•May 1, 2022•3 citations

Investigation of the thermodynamic properties and phase transitions in a strongly diluted three-vertex antiferromagnetic Potts model by the Monte Carlo method

Akai Kurbanovich Murtazaev, Albert Babaevich Babaev, G. Ya. Ataeva

The thermodynamic properties and phase transitions in a two-dimensional strongly diluted threevertex antiferromagnetic Potts model on a triangular lattice have been investigated using the Monte Carlo method. The systems with linear dimensions of L × L = N , where L = 18–48, have been considered. It has been shown using the method of fourth-order Binder cumulants that, upon the introduction of nonmagnetic impurities into the spin system described by the two-dimensional antiferromagnetic Potts model, the firstorder phase transition changes to a second-order phase transition.

Physics of the Solid State•Jan 1, 2017•6 citations

Computer Simulation of the Phase Transitions in Three-Dimensional Weakly Diluted Spin Systems

Akai Kurbanovich Murtazaev, Albert Babaevich Babaev

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.

Journal of Surface Investigation X-ray Synchrotron and Neutron Techniques•Apr 1, 2022•0 citations
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.
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 diluted Potts model with the number of spin states q = 3 are studied by computer simulation method. The systems with linear sizes L × L = N, L = 10–160 at spin concentrations p = 1.00, 0.80 are considered. The obtained numerical data show that the second-order phase transition takes place in the pure Potts model with the number of spin states q = 3, according to the theory. The introduction of a disorder in the form of nonmagnetic impurities (p = 0.80) in the Potts model with q = 3 conserves the second-order phase transition.
The thermodynamic properties and phase transitions in a two-dimensional strongly diluted threevertex antiferromagnetic Potts model on a triangular lattice have been investigated using the Monte Carlo method. The systems with linear dimensions of L × L = N , where L = 18–48, have been considered. It has been shown using the method of fourth-order Binder cumulants that, upon the introduction of nonmagnetic impurities into the spin system described by the two-dimensional antiferromagnetic Potts model, the firstorder phase transition changes to a second-order phase transition.
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.