Green’s function investigation of transition properties of the transverse Ising model

Abstract

With the help of the equations of motion method for the Green's function, the transition properties of ferroelectric thin films are investigated on the basis of the transverse Ising model. By decoupling the Fermi-type Green's functions to a higher order, the results beyond those of the usual mean-field approximation are obtained. The dependences of the polarizations on exchange interaction, transverse field, film thickness, and temperature are more complicated, and the polarizations become coupled with the transverse components of pseudospins via the eigenvalue equations of the Green's functions. The numerical results for phase diagrams and polarizations show that the higher decoupling approximation is better than the usual mean-field approximation. It suggests also that the usual mean-field approximation underestimates to some extent the tunneling role of the transverse Ising model and exaggerates the ferroelectric feature of thin films.