  Within the framework of mean field theory, we study the effects of
multi-surface modification on Curie temperature of ferroelectric films using
the transverse Ising model. The general nonlinear equations for Curie
temperature of multi-surface ferroelectric films with arbitrary exchange
constants and transverse fields are derived by the transfer matrix method. As
an example, we consider a film consisting of top surface layers, bulk layers
and bottom surface layers. Two types of surface modifications, modifications of
a surface exchange constant and a surface transverse field are taken into
account. The dependence of Curie temperature on the surface layer numbers, bulk
layer numbers, surface exchange constants, surface transverse fields and bulk
transverse fields is discussed.
