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arXiv:1510.06554 · Condensed Matter Physics

Numerical study of the spin-3/2 Ashkin-Teller model

Boudefla, Bekhechi, Hontinfinde

Published Sep 1, 2015• 7 citations
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Abstract

The study of the Ashkin-Teller model (ATM) of spin-3/2 on a hypercubic lattice is undertaken via Monte Carlo simulation.The phase diagrams are displayed and discussed in the physical parameter space.Rich physical properties are recovered, namely the second order transition and multicritical points.The phase diagrams have been obtained by varying the strength describing the four spin interaction and the single ion potential.This model shows a new high temperature partially ordered phase, called 〈S〉 and a new Baxter 3/2 ground state which do not exist either in the spin-1/2 ATM or in the spin-1 ATM.

DOI
10.5488/cmp.18.33703

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Journal of Materials Science Research•Dec 27, 2024•0 citations
The study of the Ashkin-Teller model (ATM) of spin-3/2 on a hypercubic lattice is undertaken via Monte Carlo simulation.The phase diagrams are displayed and discussed in the physical parameter space.Rich physical properties are recovered, namely the second order transition and multicritical points.The phase diagrams have been obtained by varying the strength describing the four spin interaction and the single ion potential.This model shows a new high temperature partially ordered phase, called 〈S〉 and a new Baxter 3/2 ground state which do not exist either in the spin-1/2 ATM or in the spin-1 ATM.
Two nonperturbative methods by means of the transfer-matrix finite-size-scaling and Monte Carlo simulations are used to investigate the spin-1 Ashkin-Teller model (ATM). We have obtained rich phase diagrams with first- and second-order phase transitions with several multicritical points of higher order. Also this model exhibits a partially ordered phase PO2{\mathrm{PO}}_{2}PO2​ which does not exist in the spin-1/2 Ashkin-Teller model (ATM). Finally, the critical behavior of this model is discussed.
L'étude du modèle Ashkin-Teller (ATM) du spin-3/2 sur un réseau cubique est effectuée par la simulation de Monte Carlo (MC). Les diagrammes de phase sont affichés et discutés dans l'espace de paramètres physiques. Des propriétés physiques riches sont récupérées, comme la transition du second ordre et les points multicritiques. Les diagrammes de phase ont étés obtenus en faisant varier l'interaction 4spins et le champ cristallin. Ce modèle montre une nouvelle phase partiellement ordonné à haute température, appelé et une nouvelle phase Baxter 3/2 qui n’existe pas ni dans l'ATM de spin-1/2, ni dans le spin-1 ATM.
In order to study the nature of phase transitions in magnetic systems, the aim of our research is to explore the S=1 and σ=3/2 states where the ferromagnetism as well as the influence of different crystal fields will be studied by the Monte Carlo method of The Ashken-Teller model which is a coupling of two Ising models with a four-component parameter. We have given some theoretical definitions related to the phase transition as well as the types of magnetism also the spin models and the simulation method. First, we identify the most stable phases in the phase diagrams at temperature T=0 by energy minimization. Then For higher temperatures, we find phase diagrams rich in ordered phases: a 3/2 Baxter phase and a 1/2 Baxter phase as well as a phase that appears neither in spin 1 nor in spin 3/2 ATM, and finally, a <σ> = 1/2 phases with 1st and 2nd order.
In order to study the effect of the anisotropy parameter on the two coupled Ising models, we propose an Ashkin-Teller model (ATM) with spin variable S=1. Using an effective-field theory, we show that near the partially ordered phase PO1{\mathrm{PO}}_{1}PO1​ that appears in spin-1/2 ATM, this model presents a new partially ordered phase PO2{\mathrm{PO}}_{2}PO2​. The anisotropy parameter introduces a first-order phase transition between different phases. However, the model exhibits a rich variety of phase diagrams and higher-order critical points.
Our Monte Carlo (MC) method has been extended to determine the type of ordering, the character of phase transitions, and positions of the tricritical points in the three-dimensional Ashkin-Teller spin-lattice model on a cubic lattice, which is an example of a system with multicomponent order parameter. The precise and detailed analyses of the system's behavior at the ends of the lines of Ising-like phase transitions are performed and the corrected phase diagram in these regions is presented and discussed. The localizations of the tricritical points are also given. The specific behavior of the Binder cumulant when crossing a bifurcation point has been discovered and interpreted. Some general conclusions on methods of investigation of the critical behavior of a system with a multicomponent order parameter are closing the paper.
This paper studies, by means of Monte Carlo simulations, an open ferromagnetic spin-3/2 Ashkin-Teller model defined on a square lattice. This model can be viewed as the superposition of two Ising models which are coupled by a four-spin interaction strength K4while in each Ising model, the nearest-neighbor interaction constant is K2. The model is here submitted to two stochastic dynamics that consist of two processes; the first one is the Glauber dynamics which simulates the contact of the system with a heat bath at temperature T and the second one is the Kawasaki dynamics which simulates the continuous energy flux into the system from an external source. The Glauber single-spin flip process happens with the probability p while the Kawasaki spin-exchange process between neighboring sites occurs with the probability q = 1− p. The temperature-dependence of the system magnetizations for fixed coupling constants and lattice anisotropy has been thoroughly investigated. Several thermodynamic phases and phase transitions have been obtained as well as multicritical points. When the Kawasaki dynamics becomes dominant, self-organized antiferromagnetic phases are generated. Several phase diagrams have been devised to illustrate model thermodynamic properties.