Abelian sandpiles Free

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.