A new, efficient algorithm for the Forest Fire Model

TL;DR

This paper introduces an efficient parallel algorithm for the Forest Fire Model, enabling large-scale analysis that reveals the model is not critical, challenging previous assumptions about its scaling behavior.

Contribution

The paper presents a new, scalable algorithm for the Forest Fire Model and demonstrates its effectiveness through large-scale numerical experiments, showing the model's non-critical nature.

Findings

The model lacks simple scaling behavior.

The new algorithm allows large-scale simulations.

The model is not critical, contrary to prior beliefs.

Abstract

The Drossel-Schwabl Forest Fire Model is one of the best studied models of non-conservative self-organised criticality. However, using a new algorithm, which allows us to study the model on large statistical and spatial scales, it has been shown to lack simple scaling. We thereby show that the considered model is not critical. This paper presents the algorithm and its parallel implementation in detail, together with large scale numerical results for several observables. The algorithm can easily be adapted to related problems such as percolation.