Effect of the inhomogeneity of substrate on wetting transitions

We study the substrate inhomogeneity effect on the wetting of a spin-1/2 Ising ferromagnetic film in an external magnetic field H, using Monte Carlo simulations. It is found that the inhomogeneity leads to the formation of clusters of positive and negative spins in each layer. However, depending on the values of H, for a fixed surface magnetic field Hs, each layer exhibits three different phases; totally wet, non wet and partially wet. In the latter case, we show the existence of three distinct configurations namely: A configuration in which the layer is partially wet with a total disconnection between clusters PWTD; a configuration in which the layer is partially wet with a partial disconnection between clusters PWPD; the configuration in which the layer is partially wet and the clusters are totally connected PWTC. Furthermore, we show that an increase of Hs values breaks the bonds connecting some clusters of the phase PWTC which leads to an expansion of the PWPD region. On the other hand, the frequency distribution and the average size of clusters are investigated in the PWTD region for fixed values of temperature T, Hs and H. Moreover, we show the existence of 3D-islands resulting from the formation of islands in each layer.