A solvable non-conservative model of Self-Organized Criticality

Details A solvable non-conservative model of Self-Organized Criticality A solvable non-conservative model of Self-Organized Criticality

2001-04-30

arxiv.org/abs/cond-mat/0104567v1

with a few changes: Europhys. Lett., 58 (2), pp. 250-256 (2002)

Physics

Condensed Matter

Statistical Mechanics

4 pages in RevTeX format (2 Figures) submitted to PRL

Scientific paper

10.1209/epl/i2002-00630-6

We present the first solvable non-conservative sandpile-like critical model of Self-Organized Criticality (SOC), and thereby substantiate the suggestion by Vespignani and Zapperi [A. Vespignani and S. Zapperi, Phys. Rev. E 57, 6345 (1998)] that a lack of conservation in the microscopic dynamics of an SOC-model can be compensated by introducing an external drive and thereby re-establishing criticality. The model shown is critical for all values of the conservation parameter. The analytical derivation follows the lines of Broeker and Grassberger [H.-M. Broeker and P. Grassberger, Phys. Rev. E 56, 3944 (1997)] and is supported by numerical simulation. In the limit of vanishing conservation the Random Neighbor Forest Fire Model (R-FFM) is recovered.

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