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

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.