Renormalization scheme for self-organized criticality in sandpile models.

We introduce a renormalization scheme of novel type that allows us to characterize the critical state and the scale invariant dynamics in sandpile models. The attractive fixed point clarifies the nature of self-organization in these systems. Universality classes can be identified and the critical exponents can be computed analytically. We obtain r =1.253 for the avalanche exponent and z =1.234 for the dynamical exponent. These results are in good agreement with computer simulations. The method can be naturally extended to other problems with nonequilibrium stationary states.