PHASE-DIAGRAMS OF TRANSVERSE ISING FILM

Applying the effective-field theory, we study the phase diagrams of a transverse Ising film. The phase diagrams show that, for J(S)/J < R(c) (R(c) is a critical value of J(S)/J), the critical temperature T(c) of the film is smaller than the bulk critical temperature T(bc) of the corresponding semi-infinite system; however, for J(S)/J > R(c), T(c) is larger than the surface critical temperature T(sc) of the semi-infinite system and as J(S)/J is increased further, T(c) (except T(c) of the film with two layers) rapidly approaches T(sc). We also calculate the critical transverse field h(c) and T(c) as a function of the film thickness.