Broken scaling in the Forest Fire Model
Statistical Mechanics
2009-11-07 v1
Abstract
We investigate the scaling behavior of the cluster size distribution in the Drossel-Schwabl Forest Fire model (DS-FFM) by means of large scale numerical simulations, partly on (massively) parallel machines. It turns out that simple scaling is clearly violated, as already pointed out by Grassberger [P. Grassberger, J. Phys. A: Math. Gen. 26, 2081 (1993)], but largely ignored in the literature. Most surprisingly the statistics not seems to be described by a universal scaling function, and the scale of the physically relevant region seems to be a constant. Our results strongly suggest that the DS-FFM is not critical in the sense of being free of characteristic scales.
Cite
@article{arxiv.cond-mat/0201306,
title = {Broken scaling in the Forest Fire Model},
author = {Gunnar Pruessner and Henrik Jeldtoft Jensen},
journal= {arXiv preprint arXiv:cond-mat/0201306},
year = {2009}
}
Comments
9 pages in RevTEX4 format (9 figures), submitted to PRE