Reentrant interface depinning from rough walls

Depinning of an interface from a rough self-affine wall delimiting an attractive substrate is described in terms of directed paths on a square lattice. Short range interactions are assumed and the phase diagram is determined by transfer matrix methods For several values of zeta(W), the roughness exponent of the wall. For all zeta(W) the Following scenario is observed. Ar a very low-temperature T, the interface is not pinned for wall attraction energies below a certain zeta(W)-dependent, nonzero threshold. This contrasts with the case of smooth walls, for which the threshold is zero. In a range of attraction energies just below the threshold, a pinning transition first occurs, as T increases, followed by a depinning one (reentrant depinning). This unusual reentrance phenomenon, in which; upon increasing T, dewetting is followed by wetting, is peculiar of self-affine roughness and does not occur, e.g., with a periodic substrate corrugation, The nature of both wetting and dewetting transitions is determined by the value of zeta(W). As found in related work, the two transitions are both continuous or both first-order, according to whether zeta(W)<1/2, or zeta(W)>1/2, respectively. The border value zeta(0) = 1/2 coincides with the intrinsic roughness of the interface in the bulk.