Reentrant Wetting Transition of a Rough Wall

A $2D$ model describing depinning of an interface from a rough, self-affine substrate, is studied by transfer matrix methods. The phase diagram is determined for several values of the roughness exponent, $\zeta_S$, of the attractive wall. For all $\zeta_S>0$ the following scenario is observed. In first place, in contrast to the case of a flat wall ($\zeta_S=0$), for wall attraction energies between zero and a $\zeta_S$-dependent positive value, the substrate is always wet. Furthermore, in a small range of attraction energies, a dewetting transition first occurs as T increases, followed by a wetting one. This unusual reentrance phenomenon seems to be a peculiar feature of self-affine roughness, and does not occur, e. g., for periodically corrugated substrates.