Dissipative Abelian sandpiles and random walks
Abstract
We show that the dissipative Abelian sandpile on a graph L can be related to a random walk on a graph that consists of L extended with a trapping site. From this relation it can be shown, using exact results and a scaling assumption, that the correlation length exponent ν of the dissipative sandpiles 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 result that ν=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.
 Publication:

Physical Review E
 Pub Date:
 March 2001
 DOI:
 10.1103/PhysRevE.63.030301
 arXiv:
 arXiv:condmat/0101024
 Bibcode:
 2001PhRvE..63c0301V
 Keywords:

 05.65.+b;
 45.70.Ht;
 05.40.Fb;
 05.45.Df;
 Selforganized systems;
 Avalanches;
 Random walks and Levy flights;
 Fractals;
 Condensed Matter  Statistical Mechanics
 EPrint:
 10 pages, 1 figure