Effect of roughness differences on the unbinding of interfaces

In recent years there has been considerable interest in the effect of disorder on the nature and universality of wetting transitions. One of the most frequently studied systems is that in which geometrical disorder is present in the form of substrate roughness. In 2D there is compelling evidence that the critical wetting transition found for a flat substrate may become first order when surface roughness is included. In particular, if the roughness exponent of the wall exceeds the anisotropy index of interface fluctuations in the bulk, then first-order wetting is found. Here we extend the investigation of roughness-induced effects to the situation in which we have unbinding of two fluctuating interfaces characterized by different roughness exponents ?₁ and ?₂ (e.g., a fluid membrane depinning from a liquid-vapor interface) in the absence of quenched disorder. In this case symmetry prevents a change in order of the unbinding transition as the rough-nesses are varied; however, the critical behavior is again found to be controlled by the larger of ?₁ and ?₂. In addition, our results depend quantitatively on a nonuniversal parameter related to the relative curvature of the two interfaces whenever ?₁ ? ?₂.