J. Phys. France
Volume 51, Numéro 11, juin 1990
Page(s) 1077 - 1098
J. Phys. France 51, 1077-1098 (1990)
DOI: 10.1051/jphys:0199000510110107700

Some more sandpiles

P. Grassberger1 et S.S. Manna2

1  Physics Department, University of Wuppertal, D-5600 Wuppertal 1, Gauss-Strasse 20, F.R.G.
2  HLRZ, c/o Forschungszentrum (KFA) Jülich, D-5170 Jülich 1, F.R.G.

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.

0550 - Lattice theory and statistics (Ising, Potts, etc.).
0570J - Critical point phenomena.

Key words
critical phenomena -- lattice theory and statistics -- percolation