Length Scales and Power Laws in the Two-Dimensional Forest-Fire Model

Abstract

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.

20 pages plain TeX, 7 figures included using psfig.sty, PostScript for the complete paper also available at http://www.physik.fu-berlin.de/~ag-peschel/papers/forest2d.ps.gz , extra software at http://www.physik.fu-berlin.de/~ag-peschel/software/forest2d.html ; main change: inclusion of further data in the determination of nu_T in Section 2.1 + some small changes; final version to appear in Physica A