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Journal of Physics C Solid State Physics

Surface phase diagrams of the Ising with a transverse field

Enaldo F. Sarmento, I. Tamura, L E M C de Oliveira, T. Kaneyoshi

Published Jun 30, 1984• 33 citations
Publisher

Abstract

Within the framework of the standard mean-field approximation and an effective-field theory with correlation the authors discuss the phase diagram for surface ordering in a semi-infinite Ising spin system with a transverse field. Although analytically simple, the effective-field theory is superior to the standard mean-field approximation. A certain characteristic behaviour is found for the surface ordering both in the standard mean-field approximation and in the effective-field theory.

DOI
10.1088/0022-3719/17/18/012

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physica status solidi (b)•Apr 16, 2003•22 citations
Within the framework of the standard mean-field approximation and an effective-field theory with correlation the authors discuss the phase diagram for surface ordering in a semi-infinite Ising spin system with a transverse field. Although analytically simple, the effective-field theory is superior to the standard mean-field approximation. A certain characteristic behaviour is found for the surface ordering both in the standard mean-field approximation and in the effective-field theory.
Within the framework of an effective-field theory with correlation evaluated for the Ising model with transverse field, the authors discuss the following cases: a diluted ferromagnetic square lattice with a transverse field; the magnetic behaviour of a transverse Ising model with diluted surface in a simple cubic lattice; and the surface magnetism of random transverse field at the surface. The surface magnetism is examined as a function of Delta =(J s /J)-1, the concentrations p and q of magnetic atoms at the surface, and Omega s and Omega b , the surface and bulk transverse field respectively. The phase diagrams for surface ordering are obtained and some characteristic behaviours of magnetism at the diluted surface are presented. The present framework is quite superior to the standard MFA, and whenever comparison is possible a satisfactory qualitative (and to a certain extent quantitative) agreement with results available in the literature is found.
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.
Abstract The phase diagram of a transverse Ising thin film is investigated by the use of two theoretical frameworks, namely the standard mean field theory and the effective field theory. The effects of the ratio p between the bulk and surface transverse fields on the critical temperature are discussed by including the modification of surface exchange interaction. Some characteristic features are found in the phase diagrams when the ratio p increases from p = 1.0. They are enhanced for the film with thickness L smaller than 5.0. In particular, the critical ratio at which the critical temperature of the film with a finite transverse field reduces to zero, being independent of L, exhibits a linear relation when it is plotted against the modification of surface exchange interaction.