HEIGHT CORRELATIONS IN THE ABELIAN SANDPILE MODEL

We study the distribution of heights in the self-organized critical state of the Abelian sandpile model on a d-dimensional hypercubic lattice. We calculate analytically the concentration of sites having minimum allowed value in the critical state. We 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.