“Self-organized” formulation of standard percolation phenomena

✍ Scribed by Peter Grassberger; Yi-Cheng Zhang

• Publisher: Elsevier Science
• Year: 1996
• Tongue: English
• Weight: 430 KB
• Volume: 224
• Category: Article
• ISSN: 0378-4371
• DOI: 10.1016/0378-4371(95)00321-5

✦ Synopsis

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