Broken scaling in the forest-fire model.
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 26, 2081 (1993)], but largely ignored in the literature. Most surprisingly, the statistics do not seem 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.
Pruessner
Gunnar
G
Department of Mathematics, Imperial College, 180 Queen's Gate, London SW7 2BZ, United Kingdom. gunnar.pruessner@physics.org
Jensen
Henrik Jeldtoft
HJ