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Broken scaling in the Forest Fire Model

Gunnar Pruessner·Henrik Jeldtoft Jensen
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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.

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Gunnar Pruessner, Henrik Jeldtoft Jensen. 2002-01-17. Broken scaling in the Forest Fire Model. https://doi.org/10.1103/physreve.65.056707

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