Self-organized criticality in forest-fire models

We review properties of the self-organized critical (SOC) forest-fire model (FFM). Self-organized critical systems drive themselves into a critical state without fine-tuning of parameters. After an introduction, the rules of the model, and the conditions for spiral shaped and SOC large-scale structures are given. For the SOC state, critical exponents and scaling relations are introduced. The existence of an upper critical dimension and the universal behavior of the model are discussed. The relations and differences between FFM and percolation systems are outlined considering an extension of the FFM into the regions beyond the critical point. The phase transitions and the different structures found in these regions are illustrated.