The capillary-wave Hamiltonian for an interface in the presence of a weakly corrugated substrate

We derive within the mean-field version of the Landau-Ginzburg -Wilson theory the expression for the capillary-wave Hamiltonian of the interface between twophases of an uniaxial ferromagnet fluctuating in the presence of a weakly corrugated, asymptotically flat substrate. The coefficients of interfacial stiffness as well as the coefficient multiplying the coupling between the ondulations of the interface and the corrugation of the substrate are shown to depend on the local distance l between the interface and the substrate. This distance dependence goes via the exponentially decaying terms which are multiplied by polynomials in l. Using this capillary-wave Hamiltonian we show that the weak corrugation of the substrate does not lead to a shift of the critical wetting temperature as compared to the flat substrate case.