Height correlations in the abelian sandpile model

Abstract

The authors study the distribution of heights in the self-organized critical state of the Abelian sandpile model on a d-dimensional hypercubic lattice. They calculate analytically the concentration of sites having minimum allowed value in the critical state. They also calculate, in the critical state, the probability that the heights, at two sites separated by a distance r, would both have minimum values and show that the lowest-order r-dependent term in it varies as r^-2d for large r.