Surface coupling effect on wetting and layering transitions

The effect of the surface coupling Js on the dependency of the layering transition temperature TL as a function of the thickness N, of a spin-1/2 Ising film, is studied using the mean field theory. It is found that for Js greater than a critical value (Jsc=1.30), the layering transition temperature decreases when the film thickness N increases for any values of the surface magnetic field Hs. While, for Js<Jsc, the behaviour of the layering transition temperature TL, as a function of N, depends strongly on the values of Hs. Indeed, we show the existence of three distinct behaviours of TL, as a function of the film thickness N, separated by two critical surface magnetic fields Hsc1 and Hsc2, namely: (i) for Hs<Hsc1, TL increases with N; (ii) for Hsc1<Hs<Hsc2, TL increases for small values of N, and decreases for large value ones; (iii) while for Hs>Hsc2, TL decreases with increasing the film thickness. Furthermore, depending on the values of Js, the wetting temperature Tw (Tw=TL when N→∞ for a given material), can be greater or smaller than the layering transition temperature of a film of thickness N of the same material.