Emergent spatial structures in critical sandpiles

Abstract

We introduce and study a new directed sandpile model with threshold dynamics and stochastic toppling rules. We show that the particle conservation law and the directed percolation like local evolution of avalanches lead to the formation of a spatial structure in the steady state, with the density developing a power-law tail away from the top. We determine the scaling exponents characterizing the avalanche distributions in terms of the critical exponents of directed percolation in all dimensions.