GENERIC SCALE-INVARIANCE AND ROUGHENING IN NOISY MODEL SANDPILES AND OTHER DRIVEN INTERFACES

From symmetry arguments we construct a simple Langevin model to describe driven interfaces such as lattice sandpile models composed of discrete grains in the presence of white noise. The model exhibits generic scale invariance (or "self-organized criticality"), with calculable exponents in all dimensions. For spatial dimensions 1 < d less-than-or-equal-to 2 it undergoes a roughening transition between two distinct phases with algebraic correlations. The transition is Kosterlitz-Thouless-like in d = 2.