Exact Enumeration of Self-Avoiding Walks on Percolation Clusters

Abstract

Abstract We study the scaling behavior of self-avoiding walks on critically dilute lattices. To this aim, we have developed a new enumeration technique, which is highly e_cient for this particular problem. It makes use of the low connectivity and the self-similar nature of the critical percolation cluster. The problem can thus be factorized, and the exponential complexity that usually a_icts exact enumeration can be avoided. This allowed us to enumerate all conformations of walks of 1000 steps for a large random sample of percolation clusters in two dimensions. The scaling exponents could thus be determined with very high precision.