Finite-size effects in the self-organized critical forest-fire model

TL;DR

This paper investigates how finite system size influences the behavior of the self-organized critical forest-fire model, revealing that it does not follow traditional finite-size scaling but instead forms patches with distinct fire dynamics.

Contribution

It demonstrates that the model's finite-size effects lead to patchy structures and different fire types, challenging conventional critical system scaling assumptions.

Findings

No finite-size scaling observed in the model

System forms patches with different tree densities

Large fluctuations occur in smaller systems

Abstract

We study finite-size effects in the self-organized critical forest-fire model by numerically evaluating the tree density and the fire size distribution. The results show that this model does not display the finite-size scaling seen in conventional critical systems. Rather, the system is composed of relatively homogeneous patches of different tree densities, leading to two qualitatively different types of fires: those that span an entire patch and those that don't. As the system size becomes smaller, the system contains less patches, and finally becomes homogeneous, with large density fluctuations in time.