Generalized Abelian sandpile model

A sufficient condition for which the particle addition operations commute in the eventual phase space of a class of sandpile models with either integral or real local heights are obtained. In case the local heights take on real numbers, the volume of the eventual phase space is found to be ≤|detΔ| under the usual Lebesgue measure, which extends the earlier result by Dhar for the integral case. The geometrical aspect of the results, including the effect on the avalanche size distribution, are also discussed. © 1994.link_to_subscribed_fulltex