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 in the antiferromagnetic ising model on a square lattice with next-nearest-neighbor interactions

Akai Kurbanovich Murtazaev, Рамазанов Магомедшейх Курбанович, Felix A. Kassan-Ogly, М. К. Бадиев

Published Dec 1, 2013• 28 citations
Publisher

Abstract

The phase transitions in the two-dimensional Ising model on a square lattice are studied using a replica algorithm, the Monte Carlo method, and histogram analysis with allowance for the next-nearest-neighbor interactions in the range 0.1 ≤ r < 1.0. A phase diagram is constructed for the dependence of the critical temperature on the next-nearest-neighbor interaction. A second-order phase transition is detected in this range and the model under study.

DOI
10.1134/s1063776113140021

Related papers

Frustrations and phase transitions in the Ising model on square lattice

Akai Kurbanovich Murtazaev, Рамазанов Магомедшейх Курбанович, Felix A. Kassan-Ogly

The phase transitions in two-dimensional antiferromagnetic Ising model are studied on a square lattice by taking the interactions of next-nearest neighbors into account. The model is investigated on basis of the replica Monte Carlo algorithm and the histogrammic analysis of data. The diagram of the critical temperature dependence on an interaction value of next-nearest neighbors is plotted. The studied model reveals the phase transition of second order and the frustration points depending on relative interaction values and magnetic field. A effect, heat capacity splitting near the frustration points, is found.

Journal of Physics Conference Series•May 15, 2014•5 citations

Phase transitions in the antiferromagnetic Ising model on a body-centered cubic lattice with interactions between next-to-nearest neighbors

Akai Kurbanovich Murtazaev, Рамазанов Магомедшейх Курбанович, Felix A. Kassan-Ogly +1 more

Phase transitions in the antiferromagnetic Ising model on a body-centered cubic lattice are studied on the basis of the replica algorithm by the Monte Carlo method and histogram analysis taking into account the interaction of next-to-nearest neighbors. The phase diagram of the dependence of the critical temperature on the intensity of interaction of the next-to-nearest neighbors is constructed. It is found that a second-order phase transition is realized in this model in the investigated interval of the intensities of interaction of next-to-nearest neighbors.

Journal of Experimental and Theoretical Physics•Jan 1, 2015•34 citations

Phase transitions in the antiferromagnetic layered Ising model on a cubic lattice

Рамазанов Магомедшейх Курбанович, Akai Kurbanovich Murtazaev

Phase transitions of the layered antiferromagnetic Ising model on a cubic lattice with allowance for intralayer next nearest neighbor interactions in the range of 0.0 ⩽ r < 1.0 have been studied on the basis of the replica algorithm by the Monte Carlo method. The character of phase transitions has been analyzed on the basis of the histogram method and the Binder cumulant method. The phase diagram of the dependence of the critical temperature on the next nearest neighbor interaction has been constructed. It has been shown that a secondorder phase transition is observed in the interval of 0.0 ⩽ r ⩽ 0.5 and for the value r = 0.9 and a first-order phase transition is observed in the interval of 0.6 ⩽ r < 0.8.

Journal of Experimental and Theoretical Physics Letters•Apr 1, 2016•27 citations

Ising Antiferromagnet with Nearest-Neighbor and Next-Nearest-Neighbor Interactions on a Square Lattice

Akai Kurbanovich Murtazaev, Рамазанов Магомедшейх Курбанович, М. К. Бадиев

The critical properties of two-dimensional antiferromagnetic Ising model in square lattice are investigated using the replica Monte-Carlo method with account of interactions of second nearest neighbors. The diagram of critical temperature dependence on an interaction value of second nearest neighbors is plotted. Static critical exponents of the heat capacity α, susceptibility γ, magnetization β, and correlation radius ν are calculated for this model using the finite-size scaling theory.

Diffusion and defect data, solid state data. Part B, Solid state phenomena/Solid state phenomena•Apr 1, 2014•0 citations

Phase Transitions in Frustrated Ising Antiferromagnet on a Body-Centered Cubic Lattice with Next-Nearest Neighbor Interactions

Akai Kurbanovich Murtazaev, Рамазанов Магомедшейх Курбанович, Djuma R. Kurbanova

The phase transitions in antiferromagnetic Ising model are studied on a body-centered cubic lattice by taking the interactions of next-nearest neighbors into account. The model is investigated on basis of the replica Monte Carlo algorithm and the histogrammic analysis of data. The diagram of the critical temperature dependence on an interaction value of next-nearest neighbors is plotted. The studied model reveals the phase transitions of second order. A static magnetic critical indices is calculated using the finite-dimensional scaling theory.

Diffusion and defect data, solid state data. Part B, Solid state phenomena/Solid state phenomena•Jul 1, 2015•0 citations

Critical properties of an antiferromagnetic Ising model on a square lattice with interactions of the next-to-nearest neighbors

Akai Kurbanovich Murtazaev, Рамазанов Магомедшейх Курбанович, М. К. Бадиев

The critical properties of an antiferromagnetic Ising model on a square lattice with interactions of the next-to-nearest neighbors are investigated by a replica Monte-Carlo method. Using the finite-size scaling theory the static critical exponents of specific heat, ordering parameter, susceptibility, correlation radius as well as the Fisher exponent are calculated. An analysis of data is performed both with and without taking into account a correction to the finite-size scaling. It was found that in the model under consideration the second order phase transition is observed. It is shown that this model belongs to the new class of universality of critical behavior.

Low Temperature Physics•Dec 1, 2011•24 citations
The phase transitions in the two-dimensional Ising model on a square lattice are studied using a replica algorithm, the Monte Carlo method, and histogram analysis with allowance for the next-nearest-neighbor interactions in the range 0.1 ≤ r < 1.0. A phase diagram is constructed for the dependence of the critical temperature on the next-nearest-neighbor interaction. A second-order phase transition is detected in this range and the model under study.
The phase transitions in two-dimensional antiferromagnetic Ising model are studied on a square lattice by taking the interactions of next-nearest neighbors into account. The model is investigated on basis of the replica Monte Carlo algorithm and the histogrammic analysis of data. The diagram of the critical temperature dependence on an interaction value of next-nearest neighbors is plotted. The studied model reveals the phase transition of second order and the frustration points depending on relative interaction values and magnetic field. A effect, heat capacity splitting near the frustration points, is found.
Phase transitions in the antiferromagnetic Ising model on a body-centered cubic lattice are studied on the basis of the replica algorithm by the Monte Carlo method and histogram analysis taking into account the interaction of next-to-nearest neighbors. The phase diagram of the dependence of the critical temperature on the intensity of interaction of the next-to-nearest neighbors is constructed. It is found that a second-order phase transition is realized in this model in the investigated interval of the intensities of interaction of next-to-nearest neighbors.
Phase transitions of the layered antiferromagnetic Ising model on a cubic lattice with allowance for intralayer next nearest neighbor interactions in the range of 0.0 ⩽ r < 1.0 have been studied on the basis of the replica algorithm by the Monte Carlo method. The character of phase transitions has been analyzed on the basis of the histogram method and the Binder cumulant method. The phase diagram of the dependence of the critical temperature on the next nearest neighbor interaction has been constructed. It has been shown that a secondorder phase transition is observed in the interval of 0.0 ⩽ r ⩽ 0.5 and for the value r = 0.9 and a first-order phase transition is observed in the interval of 0.6 ⩽ r < 0.8.
The phase transitions in antiferromagnetic Ising model are studied on a body-centered cubic lattice by taking the interactions of next-nearest neighbors into account. The model is investigated on basis of the replica Monte Carlo algorithm and the histogrammic analysis of data. The diagram of the critical temperature dependence on an interaction value of next-nearest neighbors is plotted. The studied model reveals the phase transitions of second order. A static magnetic critical indices is calculated using the finite-dimensional scaling theory.
The critical properties of an antiferromagnetic Ising model on a square lattice with interactions of the next-to-nearest neighbors are investigated by a replica Monte-Carlo method. Using the finite-size scaling theory the static critical exponents of specific heat, ordering parameter, susceptibility, correlation radius as well as the Fisher exponent are calculated. An analysis of data is performed both with and without taking into account a correction to the finite-size scaling. It was found that in the model under consideration the second order phase transition is observed. It is shown that this model belongs to the new class of universality of critical behavior.