The magnetizations and the susceptibilities in ferroelectric films described by a transverse spin-1/2 Ising model

The critical temperature in ferroelectric films described by a transverse spin-1/2 Ising model is studied using the effective field theory along with a probability distribution technique. We discuss an L layer film of simple cubic symmetry with nearest-neighbour interactions in which the strengths of the interactions are different from the bulk values in the surface layers. We derive the phase diagram, the longitudinal and transverse magnetization profiles and also the longitudinal and transverse susceptibilities. In such films, the critical temperature can shift to either lower or higher temperature compared with the corresponding bulk value. The film longitudinal susceptibility diverges at the critical temperature TC while the film transverse susceptibility presents a cusp at TC.