We suggest an approach to calculate the physical properties of ferroelectric thin films. Our approach takes into account the depolarization field and spatial inhomogeneity of the order parameter inherent to thin films. In or approach, we consider the thin film to be short circuited with the perfectly conducting electrodes and monodomain. The solution of the corresponding Euler–Lagrange equation by the direct variational method shows that the initial free-energy functional of a thin film can be reduced to some effective functional which does not include spatial derivatives of the order parameter. The coefficients of this functional, however, are renormalized as compared to those of the initial free-energy functional. We present the detailed calculation of the spontaneous polarization, pyrocoefficient, and dielectric susceptibility. We analyze in detail the spatial profile of the depolarization field with special attention to its properties near size-driven phase transition in a film.

We calculate the dynamic order parameter and dielectric susceptibility for the relaxor ferroelectrics like ${\mathrm{PbMg}}_{\mathrm{1/3}}{\mathrm{Nb}}_{\mathrm{2/3}}{\mathrm{O}}_3,$ ${\mathrm{PbSc}}_{\mathrm{1/2}}{\mathrm{Ta}}_{\mathrm{1/2}}{\mathrm{O}}_3$ and ${\mathrm{Pb}}_{\text{1−x}}{\mathrm{La}}_x{\mathrm{Zr}}_y{\mathrm{Ti}}_{\text{1−y}}{\mathrm{O}}_3.$ Calculations of temperature and frequency dependence of dielectric susceptibility show the existence of low- and high-temperature group of maxima obeyed to Vogel–Fulcher (VF) and Arrhenius laws, respectively. The VF law and non-Debye relaxation behavior as well as the stretched exponential law of susceptibility time decay were shown to be the consequence of random fields distribution which transforms single dipole Arrhenius and Debye laws into VF and non-Debye, stretched exponential laws, respectively. Comparison of observed and calculated characteristics of the relaxors is carried out.