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Journal of Experimental and Theoretical Physics

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, Djuma R. Kurbanova

Published Jan 1, 2015• 34 citations
Publisher

Abstract

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.

DOI
10.1134/s1063776115010057

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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.
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.
Abstract Phase transitions and critical properties of the antiferromagnetic Heisenberg model on a body-centered cubic lattice are investigated by the Monte Carlo method, based on the replica algorithm with allowance of the interactions between the first and second nearest neighbors. Analysis is performed for intensity ratios r of exchange interaction between the first and second nearest neighbors in the interval 0.0 ≤ r ≤ 1.0. The phase diagram of the dependence of the critical temperature on the intensity of interaction of the second nearest neighbors is constructed. On this diagram, a region in which the transition from the antiferromagnetic to the paramagnetic phase is of the first order is detected. The entire set of the main static critical indices is calculated. It is shown that the universality class of the critical behavior is preserved in the interval 0.0 ≤ r ≤ 0.6. It is found that the variation of the second nearest neighbor interaction intensity in the range 0.8 ≤ r ≤ 1.0 leads to nonuniversal critical behavior.
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.
Abstract—Phase transitions in the antiferromagnetic Heisenberg model on the body-centered cubic lattice were studied using the replica algorithm of the Monte Carlo method, taking into account the interactions between the first and second neighbors. The investigations were performed for the ratio of the value of the exchange interactions between the nearest and second neighbors in the range 0.0 ≤ r ≤ 1.0. The phase diagram of critical temperature versus the value of interaction between the second neighbors was constructed. The region in the diagram where the transition from antiferromagnetic to paramagnetic phase is of the first order was discovered for the first time in this study.
The replica Monte Carlo method has been used to investigate the critical behavior of a threedimensional antiferromagnetic Ising model on a body-centered cubic lattice, taking into account interactions of the adjacent behind neighbors. Investigations are carried out for the ratios of the values of exchange interactions behind the nearest and next nearest neighbors k = J 2/J 1 in the range of k ∈ [0.0, 1.0] with the step Δk = 0.1. In the framework of the theory of finite-dimensional scaling the static critical indices of heat capacity α, susceptibility γ, of the order parameter β, correlation radius ν, and also the Fisher index η are calculated. It is shown that the universality class of the critical behavior of this model is kept in the interval of k ∈ [0.0, 0.6]. It is established that a nonuniversal critical behavior is observed in the range k ∈ [0.8, 1.0].