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

Journal of Experimental and Theoretical Physics

Phase Transitions and Critical Phenomena in the 2D Potts Impurity Model on a Square Lattice

Akai Kurbanovich Murtazaev, Albert Babaevich Babaev, G. Ya. Ataeva, М. А. Магомедов

Published Sep 1, 2022• 4 citations
Publisher

Abstract

Abstract Phase transitions and critical behavior in the 2D dilute Potts model with number q = 4 of spin states on a square lattice are investigated by computer simulation. Systems with linear sizes L × L = N, l = 10–160 with spin concentrations p = 1.00, 0.95, 0.80 are considered. It is shown that the introduction of magnetic impurities plays a stabilizing role in the realization of a second-order phase transition in the Potts model under investigation. Based on the finite-size scaling theory, statistical critical indices of heat capacity α, susceptibility γ, magnetization β, and correlation radius index ν are calculated for the range of concentrations p considered here.

DOI
10.1134/s1063776122090072

Related papers

Critical properties of 2d disordered 3-state antiferromagnetic potts model ON TRIANGULAR LATTICE

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

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.

EPJ Web of Conferences•Jan 1, 2018•0 citations

Phase transitions in a three-dimensional diluted Potts model with 4 spin states

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

A Monte–Carlo method is used to study phase transitions and critical phenomena in a three-dimensional Potts model with 4 spin states and nonmagnetic impurities. Systems with linear sizes L=20–32 and spin concentrations p=1.00, 0.90, and 0.65 are studied. A fourth order Binder cumulant method is used to show that this model yields a second order phase transition for strong dilution with a spin concentration p=0.65, while the pure model (p=1.00) and the model with weak dilution (p=0.90) yield a first order phase transition. The static critical indices for the heat capacity α, susceptibility γ, magnetization β, and correlation radius ν are calculated using a finite-dimensional scaling theory.

Low Temperature Physics•Feb 1, 2011•13 citations

Influence of quenched nonmagnetic impurities on phase transitions in a three-dimensional diluted Potts model with spin state number q = 4

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

The influence of quenched nonmagnetic impurities on phase transitions and critical phenomena in the 3D Potts model with the spin state number q = 4 is studied using the Monte Carlo method. Systems with the linear size L = 20–32 and spin concentrations p = 1.00, 0.90, 0.65 are considered. The fourth order Binder cumulant method is used to demonstrate that in the strongly diluted regime, a phase transition of the second kind is observed in this model for the spin concentration p = 0.65, and a phase transition of the first kind is observed for the pure ( p = 1.00) and weakly diluted ( p = 0.90) models. The theory of finite-dimensional scaling is used to calculate the static critical parameters of heat capacity α, susceptibility γ, magnetization β, and correlation radius ν.

Bulletin of the Russian Academy of Sciences Physics•May 1, 2011•2 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

Phase transition properties of three-dimensional systems described by diluted potts model

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

Monte Carlo simulations are performed to analyze phase transitions in three-dimensional systems described by the 3-state Potts model with nonmagnetic impurities. Numerical results are presented for systems with spin concentrations p = 1.00, 0.95, 0.90, 0.80, 0.70, and 0.65 on lattices of size L varying between 20 and 44. Binder’s cumulant analysis shows that the introduction of quenched disorder in the form of non-magnetic impurities induces a crossover from first-order to second-order phase transition. The finite-size scaling method is used to calculate the static critical exponents α, γ, β, and ν for specific heat, susceptibility, magnetization, and correlation length, respectively.

Journal of Experimental and Theoretical Physics•Sep 1, 2009•14 citations

Phase transitions in the two-dimensional ferro- and antiferromagnetic potts models on a triangular lattice

Akai Kurbanovich Murtazaev, Albert Babaevich Babaev

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.

Journal of Experimental and Theoretical Physics•Dec 1, 2012•17 citations
Abstract Phase transitions and critical behavior in the 2D dilute Potts model with number q = 4 of spin states on a square lattice are investigated by computer simulation. Systems with linear sizes L × L = N, l = 10–160 with spin concentrations p = 1.00, 0.95, 0.80 are considered. It is shown that the introduction of magnetic impurities plays a stabilizing role in the realization of a second-order phase transition in the Potts model under investigation. Based on the finite-size scaling theory, statistical critical indices of heat capacity α, susceptibility γ, magnetization β, and correlation radius index ν are calculated for the range of concentrations p considered here.
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.
A Monte–Carlo method is used to study phase transitions and critical phenomena in a three-dimensional Potts model with 4 spin states and nonmagnetic impurities. Systems with linear sizes L=20–32 and spin concentrations p=1.00, 0.90, and 0.65 are studied. A fourth order Binder cumulant method is used to show that this model yields a second order phase transition for strong dilution with a spin concentration p=0.65, while the pure model (p=1.00) and the model with weak dilution (p=0.90) yield a first order phase transition. The static critical indices for the heat capacity α, susceptibility γ, magnetization β, and correlation radius ν are calculated using a finite-dimensional scaling theory.
The influence of quenched nonmagnetic impurities on phase transitions and critical phenomena in the 3D Potts model with the spin state number q = 4 is studied using the Monte Carlo method. Systems with the linear size L = 20–32 and spin concentrations p = 1.00, 0.90, 0.65 are considered. The fourth order Binder cumulant method is used to demonstrate that in the strongly diluted regime, a phase transition of the second kind is observed in this model for the spin concentration p = 0.65, and a phase transition of the first kind is observed for the pure ( p = 1.00) and weakly diluted ( p = 0.90) models. The theory of finite-dimensional scaling is used to calculate the static critical parameters of heat capacity α, susceptibility γ, magnetization β, and correlation radius ν.
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.
Monte Carlo simulations are performed to analyze phase transitions in three-dimensional systems described by the 3-state Potts model with nonmagnetic impurities. Numerical results are presented for systems with spin concentrations p = 1.00, 0.95, 0.90, 0.80, 0.70, and 0.65 on lattices of size L varying between 20 and 44. Binder’s cumulant analysis shows that the introduction of quenched disorder in the form of non-magnetic impurities induces a crossover from first-order to second-order phase transition. The finite-size scaling method is used to calculate the static critical exponents α, γ, β, and ν for specific heat, susceptibility, magnetization, and correlation length, respectively.
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.