MONTE-CARLO RENORMALIZATION-GROUP STUDY OF SELF-ORGANIZED CRITICALITY

We have studied a class of dynamical models exhibiting self-organized criticality, which have recently been introduced by Bak, Tang, and Wiesenfeld [Phys. Rev. Lett. 59, 381 (1987)] by the Monte Carlo renormalization-group (MCRG) technique. In particular, we estimate critical exponents for the sandpile model in dimensions d=2 and 3 by MCRG, and present numerical simulations for d=4, which is thought to be the upper critical dimension. Our results are to higher precision than, although consistent with, the original numerical work on the problem. We further compare our results to those of a recent conjecture. © 1990 The American Physical Society.