Phase transitions in the antiferromagnetic Ising model on a body-centered cubic lattice with interactions between next-t
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DISORDER, AND PHASE TRANSITION IN CONDENSED SYSTEM
Phase Transitions in the Antiferromagnetic Ising Model on a BodyCentered Cubic Lattice with Interactions between NexttoNearest Neighbors A. K. Murtazaeva,b, M. K. Ramazanova*, F. A. KassanOglyc, and D. R. Kurbanovaa a
Institute of Physics, Dagestan Research Center, Russian Academy of Sciences, Makhachkala, 367003 Russia b Dagestan State University, Makhachkala, 367025 Russia c Institute of Metal Physics, Ural Branch, Russian Academy of Sciences, Yekaterinburg, 620990 Russia *email: [email protected] Received June 9, 2014
Abstract—Phase transitions in the antiferromagnetic Ising model on a bodycentered cubic lattice are stud ied on the basis of the replica algorithm by the Monte Carlo method and histogram analysis taking into account the interaction of nexttonearest neighbors. The phase diagram of the dependence of the critical temperature on the intensity of interaction of the nexttonearest neighbors is constructed. It is found that a secondorder phase transition is realized in this model in the investigated interval of the intensities of inter action of nexttonearest neighbors. DOI: 10.1134/S1063776115010057
1. INTRODUCTION The quantitative description of phase transitions (PTs) and critical phenomena in the contemporary physics of condensed states is based on various lattice models. Theoretical methods of simple lattice mod els could be used to precisely solve only a limited number of problems. One such model is the 2D Ising model [1]. The degeneracy of the ground state and the emergence of various phases and phase transi tions are observed in the classical 3D Ising model, taking into account the antiferromagnetic interac tions of nexttonearest neighbors. In addition, the allowance for the interaction of nexttonearest neighbors can also affect the critical behavior of the model; in particular, various anomalies in critical properties appear [2]. Theoretical calculations and numerical simulation by the Monte Carlo (MC) method for the Ising model on a bodycentered cubic (bcc) lattice were performed in [3–8]. The authors of [3] analyzed the critical behavior of the Ising model on various types of lattices using the Monte Carlo method. Phasetransition tem perature and thermodynamic parameters in the criti cal region were calculated. The theoretical analysis carried out in [4, 5] also indicated that a secondorder PT takes place in the Ising model on the simple cubic and bcc lattices. Analogous results were obtained in [6–8]. In these publications, the critical indices for some thermodynamic parameters were calculated. According to the results obtained in [7, 8], the transi tion from the ferromagnetic phase to the paramagnetic
phase is a secondorder PT, while the transition from the antiferromagnetic to the paramagnetic phase is a firstorder transition. It follows hence that when the intensity of the interaction of nexttonearest neigh bors increases, the phase transition order in the system changes from the second to the first. In th
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