Exact enumeration of self-avoiding walks on percolation clusters

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 efficient 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 afflicts 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.