Critical behaviour of the Drossel-Schwabl forest fire model

We present high statistics Monte Carlo results for the Drossel-Schwabl forest fire model in two dimensions. They extend to much larger lattices (up to 65 536 x 65 536) than previous simulations and are much closer to the critical point (up to theta = p/f = 256 000). They are incompatible with all previous conjectures for the (extrapolated) critical behaviour, although in general they agree well with previous simulations wherever they can be directly compared. Instead, they suggest that scaling laws observed in previous simulations are spurious, and that the density rho of trees in the critical state was grossly underestimated. While previous simulations gave rho approximate to 408,we conjecture that rho is actually equal to the critical threshold p(c) = 0.592... for site percolation in d = 2. This is still, however, far from the densities reachable with present day computers, and we estimate that we would need many orders of magnitude higher CPU times and storage capacities to reach the true critical behaviour-which might or might not be that of ordinary percolation.