RENORMALIZATION SCHEME FOR FOREST-FIRE MODELS

We introduce a renormalization scheme for forest-fire models in order to characterize the nature of the critical state and its scale-invaria nt dynamics. We study one- and two-dimensional models defining a chara cterization of the phase space that allows us to describe the evolutio n of the dynamics under a scale transformation. We show the existence of a relevant critical parameter associated with a repulsive fixed poi nt in the phase space, From the renormalization-group point of view th ese models are therefore critical in the usual sense, because the fixe d-point value of the control parameter is crucial in order to get crit icality. This general scheme allows us to calculate analytically the c ritical exponent nu which describes the approach to the critical point along the repulsive direction and the exponent tau that characterizes the distribution of forest clusters at the critical point. We obtain nu = 1.0, tau = 1.0 and nu = 0.65, tau = 1.16, respectively, for the o ne- and two-dimensional cases, in very good agreement with exact and n umerical results.