Phenomenological theory of surface effects in ferroelectrics and its relationship with transverse Ising model

The relationship between the transverse field Ising model and the Landau phenomenological theory for ferroelectrics is analyzed, and the Landau free energy expression for ferroelectrics having surfaces is derived. It is pointed out that the traditional expression in which the surface integral has only a term of the square polarization is valid only for special cases, in general a term of the polarization to the four should be included as well. By use of the newly derived free energy expression, the thickness-dependence of the spontaneous polarization and Curie temperature of ferroelectric films is calculated; thereby some experimental results incompatible with the traditional phenomenological theory are successfully explained.