Critical line between the first-order and the second-order phase transition for ferroelectric thin films described by TIM

In this Letter, we apply the transverse-field Ising model (TIM) with a four-body interaction term to ferroelectric thin films. By defining a critical value (J′/J)c, the critical line between the first-order and the second-order phase transition is obtained for ferroelectric thin films. We discuss influence of the film thickness on the critical value (J′/J)c. Behavior of the phase transition and the dielectric susceptibility of ferroelectric thin films are investigated within the mean-field approximation.