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Journal of Physics Condensed Matter

Critical properties of Ising multilayer systems: cluster approximation

T. Kaneyoshi

Published Sep 10, 1999• 13 citations
Publisher

Abstract

The theoretical framework for investigating the critical behaviour of an Ising multilayer system consisting of alternating spin-1/2 and spin- S ( S ½) magnetic layers is given within the cluster approximation introduced into the differential operator technique. It has the statistical accuracy corresponding to the Bethe-Peierls approximation. The critical temperatures T C of some multilayer systems are studied numerically. We find some characteristic features, including the behaviour of a critical transverse field in the transverse spin-1/2 ferromagnetic multilayer system and the different behaviour of the T C curve in an alternating spin-1/2 and spin- S ( S >½) Ising multilayer system, depending on whether S is an integer or a half-integer.

DOI
10.1088/0953-8984/11/38/310

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The theoretical framework for investigating the critical behaviour of an Ising multilayer system consisting of alternating spin-1/2 and spin- S ( S ½) magnetic layers is given within the cluster approximation introduced into the differential operator technique. It has the statistical accuracy corresponding to the Bethe-Peierls approximation. The critical temperatures T C of some multilayer systems are studied numerically. We find some characteristic features, including the behaviour of a critical transverse field in the transverse spin-1/2 ferromagnetic multilayer system and the different behaviour of the T C curve in an alternating spin-1/2 and spin- S ( S >½) Ising multilayer system, depending on whether S is an integer or a half-integer.
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.
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.
The effect of a random transverse field on the phase transitions of a ferromagnetic spin 1/2 Ising film is investigated within a finite cluster approximation with an expansion technique for the cluster identities of spin 1/2 systems. The phase diagrams are determined as a function of the transverse field for different values of the concentration p of the disorder of the latter. It is found that at very low temperatures the ferromagnetic order is destroyed under the effect of the transverse field only if the concentration is larger than a critical value pc, which is independent of the film thickness.
A series of spin-cluster approximation which is a mean field type approximation is derived systematically on the basis of a spin-cluster expansion formula of the free energy. Mean field critical temperature and mean field critical coefficients are calculated by the spin-cluster approximation for the two-, three- and more than four-dimensional ferromagnetic Ising systems. Analyzing them by the coherent anomaly method, the critical temperature and the critical exponents α, β, γ and δ are estimated. Accuracy of estimated values in this method are comparable to those given by other methods such as the high temperature series analysis. The present theory provides a new and useful tool to study the critical phenomena, especially of three-dimensional systems.
The effect of surface and bulk transverse fields on the phase transitions of a semi-infinite spin-1 ferromagnetic Ising model is investigated within a finite cluster approximation with an expansion technique for cluster identities of spin-1 localized spin systems. The phase diagrams are determined as a function of the ratio of bulk and surface transverse fields, the temperature and the transverse field of the surface. They show that the systems exhibit a variety of phase transitions. A dead layer is also obtained in a special region of space parameters.