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The phase diagram of a ferroelectric thin film is studied by using the usual mean-field approximation. The crossover features, from the ferroelectric-dominant phase diagram to the paraelectric-dominant phase diagram, for the physical parameters of the thin film are discussed. Special attention is devoted to the investigation of surface and bulk layers, and how to influence the crossover values of exchange interactions and transverse fields.

Within the framework of effective-field theory with correlations, phase transition properties of ferroelectric thin films with different symmetrical surfaces described by the spin-1/2 transverse field Ising model are studied systematically by the differential operator technique. According to the coupling equations with the layer polarization average, the analytical general equations for phase diagrams of multiple-surface ferroelectric thin films with different surface layers have been derived. Then, effects of various parameter modifications on the crossover values from the FPD (ferroelectric-dominant phase diagram) to the PPD (paraelectric-dominant phase diagram) and phase transition regions in the parameter space are discussed in detail. In comparison with the mean-field approximation, the results indicate that the effective-field theory with correlations maybe reduce the ferroelectricity of the ferroelectric thin films more exaggeratedly than the mean-field approximation to some extent.

By using the usual mean-field approximation, the phase transition properties of a ferroelectric nanoparticle described by the transverse field Ising model have been studied. The exchange interactions and transverse fields at the surface are assumed to be different from those of the interactions parameters in the bulk. The phase diagrams for the ferroelectric nanoparticle with a size S are calculated in the (Tc, Js) coordinates and the (Tc, Ωs) coordinates by two types of parameter modifications. In addition, the crossover features for interactions parameters of the ferroelectric nanoparticle are also examined.