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physica status solidi (b)

Anisotropic Ashkin-Teller Model in a Transverse Field

L. Bahmad, A. Benyoussef, Hamid Ez-zahraouy A

Published Aug 1, 2001• 6 citations
Publisher

Abstract

Magnetic properties and phase diagrams of a spin-1/2 anisotropic Ashkin-Teller model in a transverse field are studied using the mean field theory. On the one hand, it is found that there exists a critical value of the transverse field Ωc/J1 above which the partially ordered phase 〈σS〉 appears at very low temperature and sufficiently large values of the four-spin interaction coefficient J4/J1. Such result is not obtained in the Ω/J1 = 0 case. On the other hand, the multicritical behaviour is also studied as a function of the transverse field Ω/J1 for selected values of the spin interaction coefficient J2/J1. However, depending on the transverse field value, and a fixed J2/J1 value, four varieties of phase diagrams are found. General formulae are established for an arbitrary coordination number q. The phase diagrams and the behaviour of the transverse and longitudinal magnetisations are given for q = 4.

DOI
10.1002/1521-3951(200108)226:2<403::aid-pssb403>3.0.co;2-3

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The spin 3/2 transverse Ising model with anisotropic crystal field on honeycomb lattice (z=3) has been studied by using the effective field theory with correlations. The general expressions for evaluating the second order phase transition temperatures are obtained. The results show that both the transverse field and crystal field have important effects on the phase diagram of the Ising system. The transition temperatures do not always fall to zero when Ω/|J|0 457. They approach a constant value 0 525 for large negative D(D→-∞) without transverse field (Ω=0). On the other hand, it is shown that all phase transformations are second order.
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 ⟩.
We investigate the phase diagram for the spin-3/23/23/2 ferromagnetic Blume-Capel model in a transverse crystal field using the standard mean-field approximation within the framework of Bogoliubov inequality for free energy. We draw a very rich phase diagram with first- and second-order transition lines; tricritical and tetracritical points; critical endpoint of order 2 and double critical endpoint. Additionally, the behaviour of magnetisation as a function of temperature over a wide range of values of both longitudinal and transverse crystal fields is also analysed. To the best of our knowledge, this quantum spin model has only been studied employing an effective field theory, which in turn was not able to characterise completely the multicritical phenomena in its phase diagram, because that procedure is not based on free energy. Thus, our findings on the phase diagram for the present model are novel as they have been not previously reported.
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.
We study the phase diagram and magnetic properties of a transverse spin-1 Ising model with random longitudinal crystal-field interactions using an expansion technique for cluster identities of spin-1 localized spin systems. Partially ordered phases appear for a particular two valued distribution P(D i )=1/2( delta (D i -(1+ alpha )D)+ delta (D i -(1- alpha )D)), and sufficiently small transverse field Omega . The longitudinal and transverse magnetizations and the quadrupolar moments are calculated. General formulae, applicable to structures with arbitrary coordination number N, are given.
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.