Magnetic properties of a transverse spin-12Ising film

Abstract

Within the framework of the effective-field theory, we examine the phase transitions of a transverse spin-$\frac{1}{2}$ Ising film. The critical temperatures of the film as a function of the interactions, transverse fields, and film thickness are studied. It is found that for the ratio of the surface interactions to the bulk ones ${R=J}_{s}/J$ less than a critical value ${R}_{c},$ the critical temperature ${T}_{c}/J$ of the film is smaller than the bulk critical temperature ${T}_{c}^{B}/J$ and as the film thickness L is increased further, ${T}_{c}/J$ increases and approaches asymptotically ${T}_{c}^{B}/J$ for large values of L. However, for $Rg{R}_{c}, {T}_{c}/J$ is larger both than the bulk ${T}_{c}^{B}/J$ and the surface ${T}_{c}^{S}/J$ critical temperatures of the corresponding semi-infinite system and as the film thickness L is increased further, ${T}_{c}/J$ decreases and approaches asymptotically, for large values of L, the surface magnetic transition ${T}_{c}^{S}/J$ observed in the corresponding semi-infinite system. We calculate also some magnetic properties of the film such as the layer magnetizations, their averages and their profiles and the longitudinal susceptibility of the film. The film longitudinal susceptibility still diverges at the film critical temperature as does the bulk longitudinal susceptibility, but its magnitude is reduced. Also there is a rounded peak at the bulk critical temperature when $Rg{R}_{c}.$ The bulk related character of the susceptibility is more pronounced and the surface related character is less pronounced when the film thickness is large.