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Etude du modèle d’Ashkin-Teller à spins mélangés S=1 et =32 sous l’effet d’anisotropies différentes par la méthode de Monte Carlo.

Zakariya Amimer

Published Jul 5, 2021• 0 citations
OpenAlex

Abstract

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.

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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.
Using Monte Carlo simulations, we have studied the critical behaviours and phase diagrams of the spin-1/2 and spin-1 Ashkin Teller model ferromagnetic thin films. In the first part: The effect of the interaction with the exchange coupling 𝐽4 is studied. The phase diagrams present different ratios of the surface exchange interaction at the special point, in which all the films thickness have the same critical temperature. First and second order transitions appears in the system. Moreover, at the special point descriptions, we found another partially ordered phase for certain values of the parameter’s interaction. Finally, the critical exponents of the surface magnetization 𝛽1𝑚 are estimated. In the second part, the effects of the crystal field 𝐷 𝐽 ⁄ 2𝑏 and four-spins coupling (𝐽4𝑠 𝐽 ⁄ 2𝑏, 𝐽4𝑏 𝐽 ⁄ 2𝑏) has been studied in details. The phase diagrams in the (𝑘𝐵𝑇𝑐 𝐽 ⁄ 2𝑏 ,𝐽2𝑠 𝐽 ⁄ 2𝑏) plane exhibits the special point, for different values of 𝐷 𝐽 ⁄ 2𝑏 and (𝐽4𝑠 𝐽 ⁄ 2𝑏, 𝐽4𝑏 𝐽 ⁄ 2𝑏). Then, we found rich phase diagrams with firstand second-order phase transitions that meet at tricritical points, that are depended on the film thickness N. Finally, this model presents a new partially ordered phase < 𝜎𝑆 >, between the paramagnetic phase and the Baxter phase, which are separated by a second-order phase transition, for positive values of 𝐷 𝐽 ⁄ 2𝑏 and for each film thickness N.
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.
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.
Régulièrement, on fait l'étude théorique de la physique statistique, en tenant compte des différents concepts liés au Magnétisme et leur type dans les matériaux. Puis nous sommes allés à décrire quelques généralités sur le terme de la transition de phase avec leur classification pour avoir le changement d’état de ces matériaux magnétique en fonction des paramètres extérieure. Cependant l’objectif de cette thèse est l’étude de modèle Ashkin-Teller à spins mélangés (3/2,1), en premier temps nous avons apprendre le diagramme de phase à l’état fondamentale par la méthode exacte où nous avons trouvé les quatre phases les plus stable, ensuite nous avons prie la phase de Baxter ferromagnétique et on étudier à l’aide de la méthode de champ moyen et nous avons vu que les résultats obtenu sont qualitativement en bon accord.
Using the recursion method, we study the phase transitions of the Ashkin–Teller model on the Bethe lattice, restricting ourselves to the case of ferromagnetic interactions. The isotropic Ashkin–Teller model and the anisotropic one are respectively investigated, and exact expressions for the free energy and the magnetization are obtained. It can be found that each of the three varieties of phase diagrams, for the anisotropic Ashkin–Teller model, consists of four phases, i.e., the fully disordered paramagnetic phase Para , the fully ordered ferromagnetic phase Ferro , and two partially ordered ferromagnetic phases ⟨σ⟩ and ⟨σ s ⟩, while the phase diagram, for the isotropic Ashkin–Teller model, contains three phases, i.e., the fully disordered paramagnetic phase Para , the fully ordered ferromagnetic phase Baxter Phase , and the partially ordered ferromagnetic phase ⟨σ s ⟩.
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.