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We introduce a Renormalization scheme for the one and two dimensionalForest-Fire models in order to characterize the nature of the critical stateand its scale invariant dynamics. We show the existence of a relevant scalingfield associated with a repulsive fixed point. This model is therefore criticalin the usual sense because the control parameter has to be tuned to itscritical value in order to get criticality. It turns out that this is not justthe condition for a time scale separation. The critical exponents are computedanalytically and we obtain $\nu=1.0$, $\tau=1.0$ and $\nu=0.65$, $\tau=1.16$respectively for the one and two dimensional case, in very good agreement withnumerical simulations.Comment: 4 pages, 3 uuencoded Postcript figure

Renormalization Group Approach to the Critical Behavior of the Forest-Fire Model