The critical properties of magnetic films

Within the framework of the transverse Ising model and by using the effective field theory with a probability distribution technique that accounts for the self spin correlations, we have studied the critical properties of an L-layer film of simple cubic symmetry in which the exchanges strength are assumed to be different from the bulk values in N_S surface layers. We derive and illustrate the expressions for the phase diagrams, order parameter profiles and susceptibility. In such films, the critical temperature can shift to either lower or higher temperature compared with the corresponding bulk value. 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.