Abelian Sandpiles on Cylinders
arXiv:2212.12579 · doi:10.1088/1751-8121/acc435
Abstract
We study here a variant of the Abelian Sandpile Model, where the playground is a cylinder of width and of circumference c. When c << w, we describe a phenomenon which has not been observed in other geometries: the probability distribution of avalanche sizes has a ladder structure, with the first step consisting of avalanches of size up to w c/2 that are essentially equiprobable, except for a small exponential tail of order about 10c. We explain this phenomenon and describe subsequent steps.
Version to appear in JPhysA