Phys. Rev. Lett. 71, 2737–2740 (1993)Self-organized critical forest-fire model: Mean-field theory and simulation results in 1 to 6 dimenisonsReceived 17 May 1993; published in the issue dated 25 October 1993 We argue that the critical forest-fire model (FFM) introduced by Drossel and Schwabl [Phys. Rev. Lett. 69, 1629 (1992)] is a critical branching process in the mean-field approximation where the number s of trees burned in a forest fire is power-law distributed with exponent τs=5/2. The mean-field model of the FFM in finite dimension is the percolation model and, as in percolation, the upper critical dimension is 6. Simulations show that the FFM becomes increasingly percolationlike with increasing dimension d and is, within error bars, fully consistent with the percolation results when d≥3. © 1993 The American Physical Society URL:
http://link.aps.org/doi/10.1103/PhysRevLett.71.2737
DOI:
10.1103/PhysRevLett.71.2737
PACS:
64.60.Ak, 05.40.+j, 05.70.Jk, 05.70.Ln
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