Phase transitions and self organized criticality of forest fires

Abstract

In this work, we study the dynamics and critical behavior of forest fire models, with a focus on the Drossel-Schwabl forest fire model (DSFFM). Through computational simulations, we analyze phase transitions in a two-dimensional lattice model, identifying three main regimes: a mixed phase, a spiral wave phase, and a self-organized critical (SOC) phase. We characterize these phases based on spatial configurations and fire-tree density relationships, revealing discontinuous transitions and hysteresis effects. In the SOC regime, we extract critical exponents for the size distribution, radius of gyration, and burning time of tree clusters, comparing our results with those from the literature. While our simulations reproduce known scaling laws, we also discuss the limitations of the DSFFM, particularly its non-universal scaling at large system sizes and time scales. Despite these limitations, the model remains a useful tool for exploring emergent phenomena in excitable systems and complex ecological dynamics