Discontinuous interface depinning from a rough wall.

Abstract

Depinning of an interface from a random self-affine substrate with roughness exponent ${\mathrm{\ensuremath{\zeta}}}_{\mathit{S}}$ is studied in systems with short-range interactions. In two dimensions transfer matrix results show that for ${\mathrm{\ensuremath{\zeta}}}_{\mathit{S}}$1/2 depinning falls in the universality class of the flat case. When ${\mathrm{\ensuremath{\zeta}}}_{\mathit{S}}$ exceeds the roughness (${\mathrm{\ensuremath{\zeta}}}_{0}$=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 ${\mathrm{\ensuremath{\zeta}}}_{0}$=0, depinning turns first order already for ${\mathrm{\ensuremath{\zeta}}}_{\mathit{S}}$\ensuremath{\gtrsim}0. Thus critical wetting may be impossible to observe on rough substrates. \textcopyright{} 1996 The American Physical Society.