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.