Theoretical Results for Sandpile Models of SOC with Multiple Topplings

Details Theoretical Results for Sandpile Models of SOC with Multiple Topplings Theoretical Results for Sandpile Models of SOC with Multiple Topplings

2000-05-21

arxiv.org/abs/cond-mat/0005340v2

Physics

Condensed Matter

Statistical Mechanics

7 pages, 1 included figure. Some typos fixed and minor changes made. To appear in Phys. Rev. E

Scientific paper

10.1103/PhysRevE.62.5347

We study a directed stochastic sandpile model of Self-Organized Criticality, which exhibits recurrent, multiple topplings, putting it in a separate universality class from the exactly solved model of Dhar and Ramaswamy. We show that in the steady-state all stable states are equally likely. Then we explicitly derive a discrete dynamical equation for avalanches on the lattice. By coarse-graining we arrive at a continuous Langevin equation for the propagation of avalanches and calculate all the critical exponents characterizing them. The avalanche equation is similar to the Edwards-Wilkinson equation, but with a noise amplitude that is a threshold function of the local avalanche activity, or interface height, leading to a stable absorbing state when the avalanche dies. It represents a new type of absorbing state phase transition.

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