Forest fires and other examples of self-organized criticality

TL;DR

This paper reviews the self-organized critical forest-fire model, explaining its properties, critical behavior, and universality, supported by simulations and analytical insights, and discusses related SOC models.

Contribution

It provides a comprehensive review of the SOC forest-fire model, including its rules, critical exponents, scaling relations, and modifications, highlighting its universality and broader relevance.

Findings

Critical exponents and scaling relations are established.

The model exhibits an upper critical dimension.

Universality holds under various modifications.

Abstract

We review the properties of the self-organized critical (SOC) forest-fire model. The paradigm of self-organized criticality refers to the tendency of certain large dissipative systems to drive themselves into a critical state independent of the initial conditions and without fine-tuning of the parameters. After an introduction, we define the rules of the model and discuss various large-scale structures which may appear in this system. The origin of the critical behavior is explained, critical exponents are introduced, and scaling relations between the exponents are derived. Results of computer simulations and analytical calculations are summarized. The existence of an upper critical dimension and the universality of the critical behavior under changes of lattice symmetry or the introduction of immunity are discussed. A survey of interesting modifications of the forest-fire model is given. Finally, several other important SOC models are briefly described.