Dissipative Abelian Sandpiles and Random Walks

Details Dissipative Abelian Sandpiles and Random Walks Dissipative Abelian Sandpiles and Random Walks

2001-01-03

arxiv.org/abs/cond-mat/0101024v1

Physics

Condensed Matter

Statistical Mechanics

10 pages, 1 figure

Scientific paper

10.1103/PhysRevE.63.030301

We show that the dissipative Abelian sandpile on a graph L can be related to a random walk on a graph which consists of L extended with a trapping site. From this relation it can be shown, using exact results and a scaling assumption, that the dissipative sandpiles' correlation length exponent \nu always equals 1/d_w, where d_w is the fractal dimension of the random walker. This leads to a new understanding of the known results that \nu=1/2 on any Euclidean lattice. Our result is however more general and as an example we also present exact data for finite Sierpinski gaskets which fully confirm our predictions.

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