LENGTH SCALES AND POWER LAWS IN THE 2-DIMENSIONAL FOREST-FIRE MODEL

We re-examine a two-dimensional forest-fire model via Monte-Carlo simu lations and show the existence of two length scales with different cri tical exponents associated with clusters and with the usual two-point correlation function of trees. We check resp. improve previously obtai ned values for other critical exponents and perform a first investigat ion of the critical behaviour of the slowest relaxational mode. We als o investigate the possibility of describing the critical point in term s of a distribution of the global density. We find that some qualitati ve features such as a temporal oscillation and a power law of the clus ter-size distribution can nicely be obtained from such a model that di scards the spatial structure.