Exact Results for the One-Dimensional Self-Organized Critical Forest-Fire Model

1993/10/14 by Barbara Drossel, Siegfried Clar, Franz Schwabl · 3 citations
Mathematics · Physics and Astronomy · #Complex Network Analysis Techniques #Stochastic processes and statistical mechanics #Theoretical and Computational Physics #cond-mat

paper · pdf · doi:10.1103/physrevlett.71.3739

12 pages REVTEX, 2 figures upon request, dro/93/3

arxiv created 1993/10/14 · openalex publication_date 1993/12/06 · arxiv updated 2009/11/30 · openalex created_date 2016/06/24 · openalex updated_date 2026/07/28

Abstract

We present the analytic solution of the self-organized critical (SOC) forest-fire model in one dimension proving SOC in systems without conservation laws by analytic means. Under the condition that the system is in the steady state and very close to the critical point, we calculate the probability that a string of n neighboring sites is occupied by a given configuration of trees. The critical exponent describing the size distribution of forest clusters is exactly τ= 2 and does not change under certain changes of the model rules. Computer simulations confirm the analytic results.

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