Effect of roughness differences on the unbinding of interfaces

In recent years there has been considerable interest in the effect of disor der 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 tha t the critical wetting transition found for a flat substrate may become fir st order when surface roughness is included. In particular. if the roughnes s exponent of the wall exceeds the anisotropy index of interface fluctuatio ns in the bulk, then first-order wetting is found. Here we extend the inves tigation of roughness-induced effects: to the situation in which we have un binding of two fluctuating interfaces characterized by different roughness exponents zeta (1) and zeta (2) (e.g., a fluid membrane depinning from a li quid-vapor interface) in the absence of quenched disorder. In this case sym metry prevents a change in order of the unbinding transition as the roughne sses are varied; however, the critical behavior is again found to be contro lled by the larger of zeta (1) and zeta (2). In addition, our results depen d quantitatively on a nonuniversal parameter related to the relative curvat ure of the two interfaces whenever zeta (1) not equal zeta (2).