Phase Transitions in a Forest-Fire Model

Details Phase Transitions in a Forest-Fire Model Phase Transitions in a Forest-Fire Model

1997-01-09

arxiv.org/abs/cond-mat/9701062v1

Phys. Rev. E 55, 2174 (1997).

Physics

Condensed Matter

Statistical Mechanics

30 pages RevTeX, 9 PostScript figures (Figs. 1,2,4 are of reduced quality), to appear in Phys. Rev. E

Scientific paper

10.1103/PhysRevE.55.2174

We investigate a forest-fire model with the density of empty sites as control parameter. The model exhibits three phases, separated by one first-order phase transition and one 'mixed' phase transition which shows critical behavior on only one side and hysteresis. The critical behavior is found to be that of the self-organized critical forest-fire model [B. Drossel and F. Schwabl, Phys. Rev. Lett. 69, 1629 (1992)], whereas in the adjacent phase one finds the spiral waves of the Bak et al. forest-fire model [P. Bak, K. Chen and C. Tang, Phys. Lett. A 147, 297 (1990)]. In the third phase one observes clustering of trees with the fire burning at the edges of the clusters. The relation between the density distribution in the spiral state and the percolation threshold is explained and the implications for stationary states with spiral waves in arbitrary excitable systems are discussed. Furthermore, we comment on the possibility of mapping self-organized critical systems onto 'ordinary' critical systems.

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