Ferroelectric phase transitions of nanoislands based on transverse ising model

Based on the transverse field Ising model, the phase transition properties of nanoislands with a spin-1/2 are studied by using the usual decoupling approximation of Fermi-type Green's function. The phase diagram indicates that the phase transition curve (J S /J = t c , omega S /J similar to t c ) is highly sensitive to the interlayer exchange interaction (J R /J) and the ratio of surface to center transverse fields (omega S /omega). The polarization diagram reveals that the polarization curve exhibits steps attributed to spin inversion, and the temperature of the step point corresponds to the temperature at which spin configuration changes.