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Journal of Experimental and Theoretical Physics Letters

Phase Diagram of the Antiferromagnetic Heisenberg Model on a Cubic Lattice

Рамазанов Магомедшейх Курбанович, Akai Kurbanovich Murtazaev

Published May 1, 2019• 17 citations
Publisher

Abstract

Phase transitions in the antiferromagnetic Heisenberg model on a cubic lattice with intralayer next-nearest neighbor interactions are studied using the replica Monte Carlo algorithm. The magnitude of next-nearest neighbor interactions varies in the range of 0.0 ≤ r ≤ 1.0. The characteristics of the phase transitions are analyzed by the histogram and Binder cumulant techniques. The phase diagram relating the transition temperature and the magnitude of next-nearest neighbor interactions is constructed. It is shown that a second order phase transition occurs in the r range under study. In this model, it is found that the intralayer next-nearest neighbor interactions do not change the order of the phase transition.

DOI
10.1134/s0021364019090121

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Phase transitions in the antiferromagnetic Heisenberg model on a cubic lattice with intralayer next-nearest neighbor interactions are studied using the replica Monte Carlo algorithm. The magnitude of next-nearest neighbor interactions varies in the range of 0.0 ≤ r ≤ 1.0. The characteristics of the phase transitions are analyzed by the histogram and Binder cumulant techniques. The phase diagram relating the transition temperature and the magnitude of next-nearest neighbor interactions is constructed. It is shown that a second order phase transition occurs in the r range under study. In this model, it is found that the intralayer next-nearest neighbor interactions do not change the order of the phase transition.
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.
Phase transitions and critical properties in the antiferromagnetic Heisenberg model on a layered cubic lattice with allowance for intralayer next nearest neighbor interactions have been studied using the replica Monte Carlo algorithm. The character of phase transitions has been analyzed using the histogram method and the Binder cumulant method. It has been found that a transition from the collinear to paramagnetic phase in the model under study occurs as a second order phase transition. The statistical critical exponents of the specific heat α, susceptibility γ, order parameter β, and correlation radius ν, as well as the Fisher index η, have been calculated using the finite-size scaling theory. It has been shown that the three-dimensional Heisenberg model on the layered cubic lattice with allowance for the next nearest neighbor interaction belongs to the same universality class of the critical behavior as the antiferromagnetic Heisenberg model on a layered triangular lattice.
Phase transitions and critical characteristics of the layered antiferromagnetic Ising model in the case of a cubic lattice with next-nearest-neighbor intralayer interactions are studied in the framework of the Monte Carlo method implementing the replica algorithm. The characteristics of the phase transitions are analyzed within the histogram method and with the Binder cumulants. For the model under study, it is found that the transition from the superantiferromagnetic phase to the paramagnetic one is a second order phase transition. The static critical exponents for the specific heat α, susceptibility γ, order parameter β, correlation radius ν, and the Fisher exponent η are calculated using the finite-size scaling theory. It is shown that the three-dimensional Ising model for the cubic lattice with next-nearest-neighbor interactions belongs to the same universality class of critical behavior as the completely frustrated three-dimensional Ising model.
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.
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 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.