Dissipative Abelian Sandpiles and Random Walks
arXiv:cond-mat/0101024 · doi:10.1103/PhysRevE.63.030301
Abstract
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 νalways 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 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.
10 pages, 1 figure
References in corpus (7)
- Dynamics of a ferromagnetic domain wall: avalanches, depinning transition and the Barkhausen effect
- Driving, conservation and absorbing states in sandpiles
- Multifractal scaling in the Bak-Tang-Wiesenfeld Sandpile and edge events
- Rare events and breakdown of simple scaling in the Abelian sandpile
- Random Neighbor Theory of the Olami-Feder-Christensen Earthquake Model
- From waves to avalanches: two different mechanisms of sandpile dynamics
- Analysis of a dissipative model of self-organized criticality with random neighbors