Crossover from Percolation to Self-Organized Criticality

TL;DR

This paper investigates how introducing immunity against fire in a forest-fire model causes a transition from percolation behavior to self-organized criticality, supported by scaling theory and simulations.

Contribution

It introduces immunity as a new parameter and demonstrates a crossover from percolation to self-organized criticality at a critical immunity level.

Findings

Clusters match percolation clusters at critical immunity

Critical exponents remain unchanged below critical immunity

System exhibits a crossover behavior

Abstract

We include immunity against fire as a new parameter into the self-organized critical forest-fire model. When the immunity assumes a critical value, clusters of burnt trees are identical to percolation clusters of random bond percolation. As long as the immunity is below its critical value, the asymptotic critical exponents are those of the original self-organized critical model, i.e. the system performs a crossover from percolation to self-organized criticality. We present a scaling theory and computer simulation results.