SELF-ORGANIZED FORMULATION OF STANDARD PERCOLATION PHENOMENA

We consider standard percolation processes such as epidemic processes with or without immunization. We show that their dynamics can be formu lated so that they mimic self-organized critical phenomena: the wettin g probability p needs not to be fine tuned to its critical value p(c) in order to arrive at criticality, but it rather emerges as a singular ity in some time-dependent distribution. On the one hand, this casts d oubts on the significance of self-organized as opposed to ordinary cri ticality. On the other hand, it suggests very efficient algorithms whe re percolation problems are studied at several values of p in a single run. As an example, we apply such an algorithm to directed percolatio n in 2 + 1 dimensions, where it allows a very precise determination of critical behavior.