Discontinuous interface depinning from a rough wall

Depinning of an interface from a random self-affine substrate with roughness exponent ${\mathrm{\zeta }}_{\mathit{S}}$ is studied in systems with short-range interactions. In two dimensions transfer matrix results show that for ${\mathrm{\zeta }}_{\mathit{S}}$${\mathrm{\zeta }}_{\mathit{S}}$ exceeds the roughness (${\mathrm{\zeta }}_0$=1/2) of the interface in the bulk, geometrical disorder becomes relevant and, moreover, depinning becomes discontinuous. The same unexpected scenario, and a precise location of the associated tricritical point, are obtained for a simplified hierarchical model. It is inferred that, in three dimensions, with ${\mathrm{\zeta }}_0$=0, depinning turns first order already for ${\mathrm{\zeta }}_{\mathit{S}}$≳0. Thus critical wetting may be impossible to observe on rough substrates. © 1996 The American Physical Society.