Phase Transitions in a Forest-Fire Model

TL;DR

This paper studies a forest-fire model revealing three distinct phases with different critical behaviors, phase transitions, and spatial patterns, linking these to known models and discussing broader implications for critical phenomena.

Contribution

It introduces a forest-fire model with a control parameter that exhibits multiple phase transitions, including a mixed transition with unique critical and hysteresis properties, connecting to existing models.

Findings

Identification of three phases with distinct behaviors

Observation of a mixed phase transition with criticality on one side

Relation between spiral states and percolation threshold

Abstract

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.