Length Scales and Power Laws in the Two-Dimensional Forest-Fire Model

TL;DR

This paper investigates a two-dimensional forest-fire model, revealing two distinct length scales with different critical exponents, and explores the model's critical behavior and cluster distributions through Monte Carlo simulations.

Contribution

It identifies two separate length scales with unique critical exponents and examines the critical behavior of the slowest relaxational mode in the forest-fire model.

Findings

Existence of two length scales with different critical exponents

Improved estimates of critical exponents from previous studies

Qualitative features like oscillations and power-law cluster distributions are captured

Abstract

We re-examine a two-dimensional forest-fire model via Monte-Carlo simulations and show the existence of two length scales with different critical exponents associated with clusters and with the usual two-point correlation function of trees. We check resp. improve previously obtained values for other critical exponents and perform a first investigation of the critical behaviour of the slowest relaxational mode. We also investigate the possibility of describing the critical point in terms of a distribution of the global density. We find that some qualitative features such as a temporal oscillation and a power law of the cluster-size distribution can nicely be obtained from such a model that discards the spatial structure.