Scaling laws and simulation results for the self-organized critical forest-fire model

We discuss the properties of a self-organized critical forest-fire model which has been introduced recently [B. Drossel and F. Schwabl, Phys. Rev. Lett. 69, 1629 (1992)]. We derive scaling laws and define critical exponents. The values of these critical exponents are determined by computer simulations in one to eight dimensions. The simulations suggest a critical dimension ${\mathit{d}}_{\mathit{c}}$=6 above which the critical exponents assume their mean-field values. Changing the lattice symmetry and allowing trees to be immune against fire, we show that the critical exponents are universal.