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Universal Journal of Physics and Application

The Critical Properties of Anisontropic Ising Model with Competing Interactions in the Region of Transition from Modulated Phase into Paramagnetic

Murtazaev Akai Kurbanovich, Ibaev Zhavrail Gadzhievich

Published Apr 1, 2016• 0 citations
Publisher

Abstract

The anisotropic Ising model with competing interactions in the region of transition from a modulated phase into paramagnetic state is investigated by the Monte-Carlo methods. By means of histogram analysis and the finite-size scaling method, the modulated – paramagnetic phase transition is shown to be a second order phase transition. Critical parameters and temperatures of phase transitions in this region are calculated.

DOI
10.13189/ujpa.2016.100201

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The anisotropic Ising model with competing interactions in the region of transition from a modulated phase into paramagnetic state is investigated by the Monte-Carlo methods. By means of histogram analysis and the finite-size scaling method, the modulated – paramagnetic phase transition is shown to be a second order phase transition. Critical parameters and temperatures of phase transitions in this region are calculated.
Abstract Monte Carlo methods are used to study the anisotropic Ising model with competing interactions in the region of the phase transition from the modulated to the paramagnetic phase. Using histogram analysis of Monte Carlo data and the theory of finite-size scaling, it is shown that the transition from the modulated state to the paramagnetic one is a second-order phase transition. The critical parameters and temperatures of phase transitions in this region are calculated. It is shown that the modulated–paramagnetic phase transition cannot be described within the framework of the known universality classes of critical behavior.
Abstract The two-dimensional anisotropic Ising model with competing interactions in the region of a transition from the ferromagnetic to paramagnetic phase has been studied by the Monte Carlo method using the Wang–Landau algorithm. State density distributions have been obtained and the order parameters corresponding to different energies have been calculated. The temperature dependences of the thermodynamic parameters including the internal energy, magnetization, free energy, entropy, specific heat at constant magnetization, and Binder cumulants have been calculated. Using the Binder cumulant method and histogram analysis, it has been shown that a single second-order phase transition from the ferromagnetic to paramagnetic phase occurs at two exchange coupling constants ratios |J1/J| = 0.1 and 0.2 in the two-dimensional anisotropic next-nearest neighbor Ising model. The phase transition temperatures have been calculated. The main critical exponents have been determined using the finite-size scaling theory.
The critical properties of the anisotropic Ising model with competing interactions have been investigated by Monte Carlo methods. The region of localization of the Lifshitz point on the phase diagram has been computed. Relations of the finite-size scaling theory are used to calculate the critical exponents of the heat capacity, susceptibility, and magnetization at various values of the competing interaction parameter J 1. A crossover to a critical behavior characteristic of a multicritical point with increasing parameter J 1 is shown to be present in the system.
Abstract A two-dimensional anisotropic Ising model with competing interactions on a square lattice is investigated using the Monte Carlo approach, based on the Wang–Landau algorithm. The curves of the density-of-states distribution and the order parameter are obtained. It is shown that the density-of-states distribution jumps sharply when |J1/J| = 0.6, due to strong degeneration of the modulated state. Sharp jumps are also observed on the distributions of the order parameter when |J1/J| > 0.2, testifying to the system’s transition from a homogeneous ordered state to a modulated phase.
Phase transitions in magnetic systems are studied using a Monte Carlo computer simulation method. The fundamentals of the technique are described and the strengths and limitations of this approach are discussed. Comparisons are made between the Monte Carlo data and exact results for the Ising square lattice. The properties of several different types of anisotropic systems are determined with particular care taken near the critical temperature Tc Competing interactions between neighboring sites has the effect of shifting Tc and may, in some cases, even change the nature of the ordered magnetic state. Critical field boundaries are traced out for several antiferromagnets and we show how competing interactions may give rise to tricritical points. We also present data on systems with impurities and examine the effects of free surfaces on the phase transition. Lastly we show how the transformation from the 2-dim Ising model to its lattice-gas model equivalent allows us to study adsorbed gas monolayers.
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.