  We consider statistical mechanics models of continuous height effective
interfaces in the presence of a delta-pinning at height zero. There is a
detailed mathematical understanding of the depinning transition in 2 dimensions
without disorder. Then the variance of the interface height w.r.t. the Gibbs
measure stays bounded uniformly in the volume for any positive pinning force
and diverges like the logarithm of the pinning force when it tends to zero.
  How does the presence of a quenched disorder term in the Hamiltonian modify
this transition? We show that an arbitarily weak random field term is enough to
beat an arbitrarily strong delta-pinning in 2 dimensions and will cause
delocalization. The proof is based on a rigorous lower bound for the overlap
between local magnetizations and random fields in finite volume. In 2
dimensions it implies growth faster than the volume which is a contradiction to
localization. We also derive a simple complementary inequality which shows that
in higher dimensions the fraction of pinned sites converges to one when the
pinning force tends to infinity.
