On the scaling behavior of the abelian sandpile model

Details On the scaling behavior of the abelian sandpile model On the scaling behavior of the abelian sandpile model

1999-04-06

arxiv.org/abs/cond-mat/9904075v2

Physics

Condensed Matter

Disordered Systems and Neural Networks

4 pages, 5 figures; the new version takes into account that the radius distribution of avalanches cannot become steeper than a

Scientific paper

10.1103/PhysRevE.61.R2168

The abelian sandpile model in two dimensions does not show the type of critical behavior familar from equilibrium systems. Rather, the properties of the stationary state follow from the condition that an avalanche started at a distance r from the system boundary has a probability proportional to 1/sqrt(r) to reach the boundary. As a consequence, the scaling behavior of the model can be obtained from evaluating dissipative avalanches alone, allowing not only to determine the values of all exponents, but showing also the breakdown of finite-size scaling.

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