Surface modification in ferroelectric transitions

The author studies the phase transitions of finite and infinite ferroelectric systems using the Ising model in a transverse field. The mean-field layer approximation is used and the results for the Curie temperature are expressed in terms of general determinants. The effects of surface modification are introduced through a surface exchange constant J₀ and a surface transverse field Omega ₀. It is shown that above a critical curve in J₀- Omega ₀ space, surface polarization is possible, even when there is no phase transition in the bulk. The dependence of the Curie temperature on the film thickness is obtained for two types of surface modification.