Surface phase transitions of the transverse Ising model with modified surface–bulk coupling

Abstract

The phase diagram of the three-dimensional transverse Ising system with antiferromagnetic intrasurface J S and surface–bulk J ⊥ interactions modified with respect to the ferromagnetic bulk exchange interaction J B is studied by the use of an effective field method in the framework of a single-site cluster theory. In this investigation, the state equations are derived by means of differential operator technique. Using these coupled equations within the four-layer approximation, it has been shown that the new parameter J ⊥ strongly affects the phase diagram obtained recently in the case J ⊥ = J B. Indeed, our calculations reveal some qualitatively interesting features both in the absence and in the presence of the surface and bulk transverse fields.