Abstract
The critical behavior of spread dynamics is examined using a forest fire model. This model is characterized by long-range interactions due to flame radiation and a weighting process induced by the combustibles’ ignition energy and the flame residence time. Unlike magnetic systems, this model exhibits a non-universal phase transition. The critical exponents of the rate of spread depend both on the local interaction and on weighting. Near the transition, the exponent x of rate of spread is found to be equivalent to that of correlation time. The weighting process exhibits a new phase transition related to the heating process. This transition is analogous to the gelation transition in spin glasses.
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