Phase Transition in a Stochastic Forest Fire Model and Effects of the Definition of Neighbourhood

TL;DR

This paper investigates a stochastic forest fire model with a tunable neighborhood parameter, revealing a sharp phase transition that can be shifted, with implications for disease spread modeling and epidemic control.

Contribution

It introduces a more realistic neighborhood definition in the forest fire model and demonstrates how small parameter changes can drastically alter system behavior.

Findings

Sharp phase transition observed in the model

Neighborhood redefinition shifts the transition point

Small parameter variations can switch between endemic and epidemic states

Abstract

We present results on a stochastic forest fire model, where the influence of the neighbour trees is treated in a more realistic way than usual and the definition of neighbourhood can be tuned by an additional parameter. This model exhibits a surprisingly sharp phase transition which can be shifted by redefinition of neighbourhood. The results can also be interpreted in terms of disease-spreading and are quite unsettling from the epidemologist's point of view, since variation of one crucial parameter only by a few percent can result in the change from endemic to epidemic behaviour.