Dirt roughens real sandpiles

Abstract

It is shown that translational disorder in the interior bulk of real sandpiles is a relevant perturbation on self-organized surface fluctuations. In two simplified models, this disorder destroys the flat phase of the surface; surface fluctuations are instead described at long wavelengths for all parameter values by a simple diffusion equation with noise, which implies a logarithmically rough surface in d=2. This result suggests that real sandpiles may also be described by a simple diffusion equation, and proves that bulk translational disorder is important for their surface fluctuations.