Abstract
We study a stochastic forest fire model introduced by P. Baket al. as a model showing self-organized criticality. This model involves a growth parameterp, and the criticality is supposed to show up in the limitp→0. By simulating the model on much larger lattices, and with much smaller values ofp, we find that the correlations with longest range do not show a nontrivial critical phenomenon in this limit, though we cannot rule out percolation-like critical behavior on a smaller but still divergent length scale. In contrast, the model shows nontrivialdeterministic evolution over time scales ≫1/p in the limitp→0.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
P. Bak, C. Tang, and K. Wiesenfeld,Phys. Rev. Lett. 59:381 (1987);Phys. Rev. A 38:364 (1988); C. Tang and P. Bak,Phys. Rev. Lett. 60:2347 (1988);J. Stat. Phys. 51:797 (1988).
P. Bak and K. Chen,Physica D 38:5 (1989).
P. Bak, K. Chen, and C. Tang, preprint (1988).
P. Dutta P. M. Horn,Rev. Mod. Phys. 53:497 (1981); M. B. Weissman,Rev. Mod. Phys. 60:537 (1988).
E. Marinari, G. Parisi, D. Ruelle, and P. Windey,Commun. Math. Phys. 81:1 (1981); E. W. Montroll and M. F. Shlesinger,Proc. Natl. Acad. Sci. USA 79:3380 (1982).
D. Wilkinson and J. F. Willemsen,J. Phys. A 16:3365 (1983).
T. Vicsek,Fractal Growth Phenomena (World Scientific, Singapore, 1989).
S. Broadbent and J. Hammersley,Math. Proc. Camb. Phil. Soc. 53:629 (1957).
P. Grassberger,Math. Biosci. 62:157 (1983);J. Phys. A 18:L215 (1985).
T. M. Liggett,Interacting Particle Systems (Springer, New York 1985).
P. Grassberger, inFractals in Physics, L. Pietronero and E. Tosatti, eds. (North-Holland, Amsterdam, 1986), p. 273.
D. Stauffer,Introduction to Percolation Theory (Taylor and Francis, London, 1985).
N. Wiener and A. Rosenblueth,Arch. Inst. Cardiol. Mex. 16:205 (1946).
P. Grassberger,J. Phys. A 19:1681 (1986).
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Grassberger, P., Kantz, H. On a forest fire model with supposed self-organized criticality. J Stat Phys 63, 685–700 (1991). https://doi.org/10.1007/BF01029205
Received:
Revised:
Issue Date:
DOI: https://doi.org/10.1007/BF01029205