Scaling laws and simulation results for the self--organized critical forest--fire model

TL;DR

This paper investigates a self-organized critical forest-fire model, deriving scaling laws and critical exponents through simulations across multiple dimensions, revealing a critical dimension and universality of exponents.

Contribution

It introduces a comprehensive analysis of the model's scaling laws, critical exponents, and universality, including the identification of a critical dimension.

Findings

Critical dimension identified as d_c=6.

Critical exponents are universal across different lattice symmetries.

Mean-field behavior observed above the critical dimension.

Abstract

We discuss the properties of a self--organized critical forest--fire model which has been introduced recently. We derive scaling laws and define critical exponents. The values of these critical exponents are determined by computer simulations in 1 to 8 dimensions. The simulations suggest a critical dimension $d_c=6$ above which the critical exponents assume their mean--field values. Changing the lattice symmetry and allowing trees to be immune against fire, we show that the critical exponents are universal.