Pinning by directed percolation

We propose directed percolation as a generic mechanism for interface pinning in a two-dimensional medium with quenched point disorder. The roughness of the interface just below a critical depinning transition is found to obey a power law with an exponent ζc=ν_⊥/ν_∥≃0.63. A moving interface near the transition is not self-affine, but may nevertheless be assigned an effective roughness exponent comparable to the values determined in fluid displacement experiments in porous media.