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Magnetic properties of a mixed spin- 1 and spin- 3 transverse Ising model

Noureddine Benayad, A. Dakhama, J. Zittartz

Published Jan 1, 1996• 0 citations
OpenAlex

Abstract

A theoretical study of a mixed spin- and spin- Ising system with independent transverse fields is present- ed using an effective field method within the framework of a single-site cluster theory. In this approach the effective field equations are derived using a probability distribution method based on the use of generalized van der Waerden identities accounting exactly for the single-site kinematic relations. The effect of the transverse fields on the critical behaviour is studied. The thermal dependence of the lon- gitudinal and transverse components of the magnetization and its higher moments is also studied.

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A theoretical study of a mixed spin- and spin- Ising system with independent transverse fields is present- ed using an effective field method within the framework of a single-site cluster theory. In this approach the effective field equations are derived using a probability distribution method based on the use of generalized van der Waerden identities accounting exactly for the single-site kinematic relations. The effect of the transverse fields on the critical behaviour is studied. The thermal dependence of the lon- gitudinal and transverse components of the magnetization and its higher moments is also studied.
Abstract The transverse spin‐3/2 Ising model with random interactions is studied using an effective field method within the framework of a single‐site cluster theory. The effective field equations are derived using a probability distribution method based on the use of generalized Van der Waerden identities, that account exactly for the single‐site kinematic relations. A model is adopted in which the nearest‐neighbour exchange couplings are described by the probability distribution law: P(Jij) = p δ(Jij‐J) + (1‐p) δ(Jij‐aJ). The critical temperature at which the longitudinal magnetization vanishes is studied as a function of p and the transverse field strength. The thermal variation of the longitudinal and transverse magnetizations and higher‐order magnetization moments are also studied.
The two dimensional mixed spin system consisting of spin-1/2 and spin-1 with four-spin interactions exhibits tricritical behaviour. The influence of a transverse field on this behaviour is studied with the finite cluster approximation based on a single-site cluster theory. The state equations are derived for the square lattice. It has been shown that the system keeps its tricritical behaviour, but when the strength of the transverse field approaches a critical value, all transitions become of second-order for any value of four-spin interaction.
Using the effective field theory (EFT) which takes into consideration the fluctuations of the effective field and which is based on a probability distribution of random variables which accounts for all the single kinematic relations, we have studied the transverse random field Ising model (TRIM) with spin-½ and spin-1 and the transverse random field mixed Ising model (TRMIM) with both spin-½ and spin-1. It is shown that the simplest approximation gives satisfactory results for the phase diagrams when compared with other methods.
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.