Anomalous scaling in the Bak-Chen-Tang forest fire model

Publisher Website
Google Scholar
Abstract
We reconsider a model introduced by Bak, Chen, and Tang [Phys. Rev. A 38, 364 (1988)] as a supposedly self-organized critical model for forest fires. We verify again that the model is not critical in two dimensions, as found also by previous authors. But we find that the model does show anomalous scaling (i.e., is critical in the sense of statistical mechanics) in three and four dimensions. We argue that this is due to the fact that fire fronts in more than two dimensions typically contain large holes which allow for large unburnt clusters to survive such fronts. These clusters then allow the next fire to pass earlier than expected naively. We claim that this is a general feature of noisy coupled relaxation oscillators with locally stable refractory states, and we relate these results to recent claims by A. Johansen [Physica D 78, 196 (1994)].