Statics of a ‘‘self-organized’’ percolation model

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Abstract
A stochastic ‘‘forest-fire’’ model is considered. Sites are filled individually at a constant mean rate; also, ‘‘sparks’’ are dropped at a small rate k, and instantaneously burn up the entire cluster they hit. I find nontrivial critical exponents in the self-organized critical limit k→0, contrary to earlier results of Drossel and Schwabl. Spatial correlation functions and a site occupancy correlation exponent are measured for the first time. Scaling relations, derived by analogy to uncorrelated percolation, are used extensively as numerical checks. Hyperscaling is violated in this system.