Self-organized criticality and the lattice topology

Abstract

We examine exhaustively the behavior of avalanches in critical height sandpile models based in two- and three-dimensional lattices of various topologies. We get that for two-dimensional lattices the spatial and temporal distributions characterizing bulk avalanches do not depend on the lattice topology. For the three-dimensional case, we detect a small dependence of the topology for the temporal distribution, while the spatial ones are independent. The two-dimensional lattices studied are: the plane ($R^2$), the cylinder ($S^1\times R$), and the M\"obius-strip ($M$); and the three-dimensional are: $R^3$, $S^1\times R^2$, $S^1\times S^1\times R$, $M\times R$, $S^2\times R$, $K\times R$, and $RP\times R$, where $K$ and $RP$ are respectively the Klein bottle and the real projective plane.