Parameter modifications in the phase diagrams of a ferroelectric nanoparticle described by the transverse field Ising model

Abstract

Within the framework of the effective-field theory (EFT) with correlations, the differential operator technique has been used to study the phase diagrams of a ferroelectric nanoparticle described by the transverse field Ising model. The dependence of the phase diagrams on two types surface parameters modifications, modifications of the surface transverse field and the surface exchange interaction, is calculated numerically in the ( T c , J s ) coordinates or the ( T c , Ω s ) coordinates. The crossover features, from the ferroelectric-dominant phase diagram (FPD) to the paraelectric-dominant phase diagram (PPD), for interaction parameters of a ferroelectric nanoparticle with a size S are determined. Meanwhile, the critical behaviours are also examined for the ferroelectric nanoparticle system.