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

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

1996-09-12

arxiv.org/abs/cond-mat/9609105v2

Physica A239 (1997) 509-530

Physics

Condensed Matter

Statistical Mechanics

20 pages plain TeX, 7 figures included using psfig.sty, PostScript for the complete paper also available at http://www.physi

Scientific paper

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.

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