Wetting phenomena on rough substrates

We consider wetting phenomena in the vicinity of rough substrates. The quenched random geometry of the substrate is assumed to be a self-affine fractal with a roughness exponent of ${\mathrm{\zeta }}_{\mathit{S}}$. Asymptotic critical properties on approaching complete and critical wetting transitions are studied by combining the replica method with scaling and renormalization-group arguments. We find new critical behavior, controlled by a zero-temperature fixed point, when ${\mathrm{\zeta }}_{\mathit{S}}$ exceeds the thermal roughness exponent of the emerging wetting layer. The possibility of an effective dimensional reduction due to randomness is considered. In two dimensions a number of exact results are obtained by using a many-body transfer-matrix technique.