Universality in the One-Dimensional Self-Organized Critical Forest-Fire Model

TL;DR

This paper demonstrates that a modified one-dimensional forest-fire model exhibits universal critical behavior in cluster and fire size distributions, confirmed through analytic calculations and computer simulations.

Contribution

It introduces a modification allowing fire jumps over small gaps and proves the universality of critical exponents in this model.

Findings

Critical exponents are the same as in the nearest-neighbor model.

Analytic calculations match computer simulation results.

The model's critical behavior is universal despite modifications.

Abstract

We modify the rules of the self-organized critical forest-fire model in one dimension by allowing the fire to jump over holes of $\le k$ sites. An analytic calculation shows that not only the size distribution of forest clusters but also the size distribution of fires is characterized by the same critical exponent as in the nearest-neighbor model, i.e. the critical behavior of the model is universal. Computer simulations confirm the analytic results.