Some more sandpiles

Abstract

For the critical sandpile model of P. Bak et al., we present high statistics results obtained by a fast non-parallel algorithm. In particular, we give results for 2, 3, 4 and 5 dimensional hypercubic lattices, and for Bethe lattices. On the latter, the model is in the same universality class as (dynamic) percolation, but the upper critical dimension seems to be 4 instead of 6 as for percolation. Between d=4 and d=6, the model seems to correspond to branched true SAW's as suggested by Obukhov. But this breaks down definitely below d=3