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We consider statistical mechanics models of continuous height effectiveinterfaces in the presence of a delta-pinning at height zero. There is adetailed mathematical understanding of the depinning transition in 2 dimensionswithout disorder. Then the variance of the interface height w.r.t. the Gibbsmeasure stays bounded uniformly in the volume for any positive pinning forceand 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 modifythis transition? We show that an arbitarily weak random field term is enough tobeat an arbitrarily strong delta-pinning in 2 dimensions and will causedelocalization. The proof is based on a rigorous lower bound for the overlapbetween local magnetizations and random fields in finite volume. In 2dimensions it implies growth faster than the volume which is a contradiction tolocalization. We also derive a simple complementary inequality which shows thatin higher dimensions the fraction of pinned sites converges to one when thepinning force tends to infinity.

Continuous interfaces with disorder: Even strong pinning is too weak in 2 dimensions