Monte-Carlo simulation on the dipole alignment in ferroelectric square lattice

The dipole alignment configuration in a multi-domained ferroelectric lattice of cubic symmetry is simulated using the Monte-Carlo method based on the Ginzburg–Landau model. It is revealed that the gradient energy associated with the spatial discontinuity of the dipole alignment near the domain walls results in not only 90°-domain configuration, but also distorted dipole alignment. The simulation shows that such a distorted alignment pattern is thermodynamically preferred at low temperature. The effect of the alignment distortion on the ferroelectric phase transition is discussed. It is found that a state number Q = 16 is enough for a reliable simulation of the distorted alignment of dipoles.