Dynamics of interface depinning in a disordered medium

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Abstract
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 ϵ= 4-D>0, where D is the interface dimension. At the transition, the dynamics is superdiffusive with a dynamical exponent z=2-2ϵ/9+O(ϵ2), and the interface height difference over a distance L grows as Lζ with ζ= ϵ/3+O(ϵ2). The interface velocity in the moving phase vanishes as (F-Fc)θ with θ=1-ϵ/9+O(ϵ2) when the driving force F approaches its threshold value Fc

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