LOCAL RIGIDITY AND SELF-ORGANIZED CRITICALITY FOR AVALANCHES

The general conditions for a sandpile system to evolve spontaneously i nto a critical state characterized by a power law distribution of aval anches or bursts are identified as: a) the existence of a stationary s tate with a global conservation law; b) long-range correlations in the continuum limit (i.e. Laplacian diffusive field); c) the existence of a local rigidity for the microscopic dynamics. These conditions permi t a classification of the models that have been considered up to now a nd the identification of the local rigidity as a new basic parameter t hat can lead to various possible scenarios ranging continuously from S OC behaviour to standard diffusion.