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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. and magnetizations in the ferroelectric nanoparticles with different structures with the effective-field theory with correlations. Very recently, Lu (7) investigated the dependence of the phase diagrams on the exchange interactions and transverse fields of a ferroelectric nanoparticle in the (Tc, Js) coordinates and the (Tc, Ωs) coordinates with the effective-field theory with correlations, however, this work has not been carried out by using the mean-field approximation up to now. In this present paper, we will study the dependence of phase diagrams on exchange interactions and transverse fields for a ferroelectric nanoparticle in the (Tc, Js) coordinates and the (Tc, Ωs) coordinates. The numerical results are compared with the corresponding results of the effective-field theory with correlations. Meanwhile, the crossover features for interactions parameters are also calculated.

Study Phase Transition Properties of a Ferroelectric Nanoparticle with the Usual Mean-Field Approximation