Self-organized criticality and directed percolation

A sandpile model with a stochastic toppling rule is studied. The control pa rameters and the phase diagram are determined through a mean-field approach , and the subcritical and critical regions are analysed. The model is found to have some similarities with directed percolation, but the existence of different boundary conditions and conservation law leads to a different uni versality class, where the critical state is extended to a line segment due to self-organization. These results are supported by numerical simulations in one dimension. This model constitutes a simple model which captures the essential difference between ordinary nonequilibrium critical phenomena, l ike directed percolation, and self-organized criticality.