Investigation of the crossover properties for the interaction parameters of a ferroelectric thin film

The crossover feature, from the ferroelectric-dominant phase diagram (FPD) to the paraelectric-dominant phase diagram (PPD), for the interaction parameters of a ferroelectric thin film described by the transverse Ising model have been calculated in detail by the use of the mean-field approximation. The crossover values of the exchange interactions and the transverse fields for a thin film with certain layers are displayed as a curved surface in the three-dimensional parameter space. The numerical results show that for thin films with different numbers of layers there exists a common intersection line for the curved surfaces of the crossover values. Meanwhile the layer-independent equation for the intersection line is obtained for the first time.