Exact solution of the one-dimensional deterministic Fixed-Energy Sandpile
Statistical Mechanics
2009-11-11 v1 Disordered Systems and Neural Networks
Abstract
In reason of the strongly non-ergodic dynamical behavior, universality properties of deterministic Fixed-Energy Sandpiles are still an open and debated issue. We investigate the one-dimensional model, whose microscopical dynamics can be solved exactly, and provide a deeper understanding of the origin of the non-ergodicity. By means of exact arguments, we prove the occurrence of orbits of well-defined periods and their dependence on the conserved energy density. Further statistical estimates of the size of the attraction's basins of the different periodic orbits lead to a complete characterization of the activity vs. energy density phase diagram in the limit of large system's size.
Cite
@article{arxiv.cond-mat/0601267,
title = {Exact solution of the one-dimensional deterministic Fixed-Energy Sandpile},
author = {Luca Dall'Asta},
journal= {arXiv preprint arXiv:cond-mat/0601267},
year = {2009}
}
Comments
4 pages, accepted for publication in Phys. Rev. Lett