  For the first time we proposed the model for the calculations of the relaxor
ferroelectrics films properties in the framework of the random field theory. We
took into account the misfit strain between film and substrate as well as
surface piezoelectric effect that causes built-in electric field in the
strained films. In the statistical theory framework we calculated random field
distribution function with the electric dipoles and monopoles as the field
sources. It was shown that with thickness decrease the mean field decreases,
while the width of the distribution function increases. This leads to the
additional smearing of the phase transition in the films in comparison to the
bulk relaxors. As an example the dependence of the order parameter and
dielectric susceptibility on the film thickness, temperature and random fields
distribution function parameters was obtained. For free standing film the
existence of critical thickness of relaxor state transformation into glassy
state was predicted. Contrary to this the appearance of misfit strain induced
ferroelectric phase appeared to be possible for some pairs film-substrate. We
have shown that susceptibility temperature maximum shift with frequency in
relaxor ferroelectric thin films obeys Vogel-Fulcher law with parameters
dependent on film thickness. For the first time the analytical dependences of
freezing temperature decreases and activation energy on the thickness was
obtained, namely freezing temperature decreases and activation energy increases
with film thickness decrease. Obtained results quantitatively agree with the
available experimental data for PbMg1/3Nb2/3O3 relaxor thin films.
