Size Effects of the Critical Temperature in Ferroelectric Thin Films

The size effects of the critical behaviors for the systems ofinteracting spins are discussed extensively in literature. In thispaper, the finite-size dependence of the critical temperature andsusceptibility of the ferroelectric thin film are investigatednumerically based on the four-state Potts model with thenearest-neighbor interactions between the dipole moments. The fourorientations of the domains exist in the ferroelectric film and themovement of the domain walls determines the polarization switchingprocess besides the boundary conditions of the film. The criticalexponents are obtained and our investigations show that the boundaryconditions play the important roles for the ferroelectricproperties of the thin films and the critical behavior of the thinfilms strongly depends on the feature of the surface.