Abelian sandpiles

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Abstract
A class of models for self-organized critical phenomena possesses an isomorphism between the recursive states under addition and the Abelian operator algebra on them. Several exact results follow, including the existence of a unique identity state, which when added to any configuration C in the recursive set relaxes back to that configuration. In this relaxation process, the number of topplings at any lattice site is independent of the configuration C.

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