Driven interfaces in quenched disorder at critical depinning

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Abstract
We reexamine the problem of interfaces driven by a bulk force in quenched disorder. We find that the Bruinsma-Aeppli equation is not compatible with the physical Hamiltonian by having one extra symmetry. We discuss the definition of the critical depinning and show that at criticality, equations with and without the nonlinear term have very different scalings. A stretched exponential law is found for the derivative distribution when lateral growth is absent.