Length scales and power laws in the two-dimensional forest-fire model

We re-examine a two-dimensional forest-fire model via Monte-Carlo simulations and show the existence of two length scales with different critical exponents associated with clusters and with the usual two-point correlation function of trees. We check resp. improve previously obtained values for other critical exponents and perform a first investigation of the critical behaviour of the slowest relaxational mode. We also investigate the possibility of describing the critical point in terms of a distribution of the global density. We find that some qualitative features such as a temporal oscillation and a power law of the cluster-size distribution can nicely be obtained from such a model that discards the spatial structure.