Dynamics of interface depinning in a disordered medium

The dynamics of a driven interface in a disordered medium close to the depinning threshold is analyzed. By a functional renormalization group scheme exponents characterizing the depinning transition are obtained to the first order in e = 4 D > 0, where D is the interface dimension. At the transition, the dynamics is superdiffusive with a dynamical exponent z = 2 2e/9 + O(e²), and the interface height difference over a distance L grows as Ll with ( = e/3 + O(e²). The interface velocity in the moving phase vanishes as (F Fc)~ with 8 = 1 e/9 + O(e²) when the driving force F approaches its threshold value P_C.