A solvable model of interface depinning in random media

We study the mean-field version of a model proposed by Leschhorn to describ e the depinning transition of interfaces in random media. We show that evol ution equations for the distribution of forces felt by the interface sites can be written directly for an infinite system. For a flat distribution of random local forces the value of the depinning threshold can be obtained ex actly. In the case of parallel dynamics (all unstable sites move simultaneo usly), due to the discrete character of the interface heights allowed in th e model, the motion of the center of mass is non-uniform in time in the mov ing phase close to the threshold, and the mean interface velocity vanishes with a square-root singularity.