Mean-Field Theory and Sandpile Models
Statistical Mechanics
2007-05-23 v1
Abstract
We review and refine the concept of a mean-field theory for the study of sandpile models, which are of central importance in the study of self-organized criticality. By considering the simple one-dimensional random walker with an absorbing and reflecting boundary we are able to construct a complete mean-field picture which we can solve in detail for different types of driving. Using this theory, we are able to clarify the effect of finite driving rate on sandpile models, as well as the observed sensitivity of certain universal quantities on the driving.
Keywords
Cite
@article{arxiv.cond-mat/0510626,
title = {Mean-Field Theory and Sandpile Models},
author = {Matthew Stapleton and Kim Christensen},
journal= {arXiv preprint arXiv:cond-mat/0510626},
year = {2007}
}
Comments
Submitted to Physical Review E