Abstract
We introduce a renormalization scheme for the one- and two-dimensional forest-fire model in order to characterize the nature of the critical state and its scale invariant dynamics. We show the existence of a relevant scaling field associated with a repulsive fixed point. This model is therefore critical in the usual sense because the control parameter has to be tuned to its critical value in order to get criticality. It turns out that this is not just the condition for a time scale separation. The critical exponents are computed analytically and we obtain nu = 1.0, tau = 1.0 and nu = 0.65, tau = 1.16, respectively, for the one- and two-dimensional cases, in very good agreement with numerical simulations.
Keywords
forest fire model, scaling, numerical simulations
Subject Categories
Renormalization (Physics), Dynamics
Disciplines
Physics
Publisher
American Physical Society
Publication Date
7-17-1995
Rights Information
©1995 American Physical Society
Rights Holder
American Physical Society
Permanent URL
Recommended Citation
Loreto, V; Pietronero, L; Vespignani, A; and Zapperi, S, "Renormalization-group approach to the critical-behavior of the forest-fire model" (1995). Physics Faculty Publications. Paper 222. http://hdl.handle.net/2047/d20002182
Click button above to open, or right-click to save.
Notes
Originally published in Physical Review Letters, v.75 no.3 (1995), pp.465-468. DOI:10.1103/PhysRevLett.75.465. Dr. Vespignani is affiliated with Northeastern University as of the time of deposit.