Forest fire as a temperature-pattern-driven depinning problem.

Abstract

A weighted isotropic forest fire model (WFFM) is introduced with an external parameter β, representing environmental factors such as inverse temperature and humidity. The spatial configuration of trees is modeled either by uncorrelated percolation with occupation probability p or by correlated percolation using the Ising model with an artificial temperature T, which controls correlations. The burning clusters are shown to exhibit a depinning transition at a p-dependent critical β_{c} (or T-dependent in the correlated case), with critically pinned states indicating that β acts as a driving force. For uncorrelated percolation, the critical exponents for nonfractal observables place the transition in the percolation universality class, while the hull fractal dimension varies from 1.34(1) at p=1 to 1.73(2) at p=p_{c}, showing that introducing correlation in the spatial structure changes the OP universality class to a new universality class for the driven interfaces. This challenges recent predictions and opens up new frontiers in our understanding concerning the effect of spatial correlations on the properties of driven interfaces.