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Journal of Physics C Solid State Physics

Mean-field theory of the semi-infinite spin-1/2 Ising model with random surface and bulk fields

M. Saber

Published Jun 30, 1987• 24 citations
Publisher

Abstract

All the possible phase diagrams of a three-dimensional semi-infinite spin-1/2 Ising model in a random field as a function of the ratio of bulk and surface interactions and the ratio of bulk and surface fields have been determined. Within the framework of the mean-field approximation eight generic types of phase diagrams can be found. It is also shown that such a system can exhibit a variety of phase transitions and multi-critical points.

DOI
10.1088/0022-3719/20/18/011

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All the possible phase diagrams of a three-dimensional semi-infinite spin-1/2 Ising model in a random field as a function of the ratio of bulk and surface interactions and the ratio of bulk and surface fields have been determined. Within the framework of the mean-field approximation eight generic types of phase diagrams can be found. It is also shown that such a system can exhibit a variety of phase transitions and multi-critical points.
As a function of the ratio R of bulk and surface interactions and the ratio D of bulk and surface crystal field we have determined, within the framework both of the mean-field approximation and by renormalization-group techniques, various types of phase diagram of a three-dimensional semi-infinite ferromagnetic spin-3/2 Blume-Capel model. We found that there exist four main types of phase diagram showing a variety of phase transitions associated with the surface and unusual multicritical topologies, including ordinary, extraordinary, surface and special phase transitions. Moreover, in the ( R , D ) plane, we determined the domains in which the system exhibits a particular type of phase diagram.
Abstract The Migdal–Kadanoff renormalization group technique is applied to study a three-dimensional semi-infinite Ising system consisting of spin-1/2 sites in the bulk and spin-1 sites at the surface. According to the competition ratio between bulk and surface exchange interactions ( R = J B / J S ), two types of surface phase diagrams have been identified in the (surface crystal field, temperature) plane. These diagrams exhibit a rich variety of phase transition phenomena: surface, ordinary, extraordinary, and special second-order transitions, first-order transitions at the surface, as well as tricritical and multicritical points. Additionally, we list in a table the fixed points that govern the observed phases and phase transitions.
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.