Reail Space Renormalization Group for Self Organized Criticality in Sandpile Models

We have introduced a new renormalization group approach that allows us to describe the critical stationary state of sandpile models (Phys. Rev. Lett. 72, 1690 (1994)). We define a characterization of the phase space in order to study the evolution of the dynamics under a change of scale. We obtain a non trivial actractive fixed point for the parameters of the model that clarifys the self organized critical nature of these models. We are able to compute the values of the critical exponents and the results are in good agreement with computer simulations. The method can be naturally extended to several other problems with non equilibrium stationary state.