A renormalization procedure for directed sandpile models

Directed models of self-organized criticality are studied in the framework of a real-space renormalization group of a different type. The identification of a suitable phase space in which to define the renormalization transformation and the coupling with the stationarity condition enables us to clarify the nature of the critical state. The renormalization equations are found to have an attractive fixed point, as expected from the self-critical nature of the model. The values of the critical exponents obtained by this procedure are in excellent agreement with exact results.