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/dw, where dw 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:cond-mat/0101024
- Bibcode:
- 2001PhRvE..63c0301V
- Keywords:
-
- 05.65.+b;
- 45.70.Ht;
- 05.40.Fb;
- 05.45.Df;
- Self-organized systems;
- Avalanches;
- Random walks and Levy flights;
- Fractals;
- Condensed Matter - Statistical Mechanics
- E-Print:
- 10 pages, 1 figure