Abelian Sandpiles on Cylinders
Statistical Mechanics
2023-04-19 v2 Mathematical Physics
math.MP
Probability
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.
Cite
@article{arxiv.2212.12579,
title = {Abelian Sandpiles on Cylinders},
author = {Jean-Pierre Eckmann and Tatiana Nagnibeda and Aymeric Perriard},
journal= {arXiv preprint arXiv:2212.12579},
year = {2023}
}
Comments
Version to appear in JPhysA