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By using the simple decoupling approximation to Fermi-type Green's function for the transverse Ising model under pseudospin theory, we systemically study the influence of different exchange interactions (transverse fields) of the two distinct materials on the polarization and Curie temperature of finite alternating superlattice. Meanwhile, we analyze the effect of the whole parameters of the top surface, present their influence on the polarization of each layer (including the mean polarization of the whole ferroelectric superlattice) and on the Curie temperature. The results show the ratio of the exchange interactions (the transverse fields), which are of the two alternating materials have deeply impact on the polarization and Curie temperature of the supperlattice. Moreover, the top surface also has great influence on the whole ferroelectric superlattice.

Based on the transverse Ising model and using decoupling approximation to the Fermi-type Green's function, we study the phase transition properties of the epitaxial ferroelectric film with one substrate. A general recursive equation of the ferroelectric thin film with two n-layer materials is obtained, which enables us to study the phase transition properties for any number layers for epitaxial ferroelectric thin film. With the help of this equation, we analyze the effect of the exchange interaction and the transverse field in the phase diagram, the influence to the polarizations and Curie temperature numerically. The results show that epitaxial ferroelectric film are able to induce a strong increase or decrease of Curie temperature to different exchange interactions and transverse fields within the epitaxial film layers. The theoretical results are in reasonable accordance with experimental data of different ferroelectric thin film.