The depinning properties of a fluctuating interface near 2D and
3D wedges with a central ridge are studied by discrete models
with short range interactions. The calculations demonstrate that,
in both cases, depinning take place in two stages: i) a
continuous filling-like transition in the pure wedge-like
components of the system; ii) a final discontinuous jump from
the central ridge. In 2D an exact transfer matrix approach shows
that, in the thermodynamic limit, the threshold of the depinning
from the central ridge coincides with the one corresponding to the
continuous filling transition. In 3D, on the contrary, accurate
Metropolis Monte Carlo simulations show that the two transitions
are separated by a finite gap. The mechanism at the basis of the
phenomenon is studied in detail and, in 2D, the whole interface
phase diagram and free energy profiles are provided. The physical
scenario emerging from these results is discussed also in relation
with the problem of the wetting transition in the case of random
rough walls.
