Critical Behaviors and Polarizations in A Transverse Ising Film

Ferroelectric thin films described by the transverse field Ising model have been studied by using the usual mean-field approximation. The critical behaviors (the critical surface transverse field and Curie temperature) and polarizations in a transverse Ising film with multi-surface layers are calculated. The main emphasis of our work is laid on the effect of surface exchange interaction on the critical surface transverse field and Curie temperature as a function of the number of surface layers. At the same time, the dependence of polarization on the Curie temperature for the ferroelectric thin film with a certain layers is also discussed in detail.