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Journal of Experimental and Theoretical Physics

Phase Transitions and Critical Properties of the Heisenberg Antiferromagnetic Model on a Body-Centered Cubic Lattice with Second Nearest Neighbor Interaction

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

Published Nov 1, 2019• 15 citations
Publisher

Abstract

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.

DOI
10.1134/s1063776119090103

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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.
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.
Abstract The Monte Carlo replica technique is used to study phase transitions and the thermodynamic and critical properties of the three-dimensional Heisenberg antiferromagnetic model on the body-centered cubic lattice with the inclusion of the interaction of the nearest and the next-nearest neighbors. The studies are performed for the proportions of the values of the exchange interactions of the nearest and the next-nearest neighbors in the range of values of k [0.0, 0.6]. The phase transition character is analyzed based on the histogram method. The overall set of static critical indices is calculated in terms of the theory of the finite-dimensional scaling. It is shown that the class of the critical behavior universality of this model is conserved in the above range of values of k.
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 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].
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 phase transitions and critical phenomena of the three-dimensional antiferromagnetic Heisenberg model on a body-centered cubic lattice with next and next-nearest neighbor interactions are studied using the replica Monte Carlo algorithm. Investigations are carried out for relations of exchange interaction values of next and next-nearest neighbors in the range of k values [0.0, 0.6]. A behavior of phase transitions is analyzed by the histogram method. A whole set of main static critical exponents is estimated within the finite-size scaling theory. The universality class of the model critical behavior is shown to be unchanged in the considered interval of k value.