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

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.