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Exact solutions for a mean-field Abelian sandpile

Steven A. Janowsky·Claude A. Laberge
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Abstract

We introduce a model for a sandpile, with N sites, critical height N and each site connected to every other site. It is thus a mean-field model in the spin-glass sense. We find an exact solution for the steady state probability distribution of avalanche sizes, and discuss its asymptotics for large N.

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Steven A. Janowsky, Claude A. Laberge. 1993-06-14. Exact solutions for a mean-field Abelian sandpile. https://doi.org/10.1088/0305-4470%2F26%2F19%2F001

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