Self-organized criticality and interface depinning transitions

We discuss the relation between self-organized criticality and depinning transitions by mapping sandpile models to equations that describe driven interfaces in random media. This equivalence yields a continuum description and gives insight about various ways of reaching the depinning critical point: slow drive (self-organized criticality), fixed density simulations, tuning the interface velocity (extremal drive criticality), or tuning the driving force. We obtain a scaling relation for the correlation length exponent for sandpiles.