Exact enumeration of self-avoiding walks on critical percolation clusters in 2–7 dimensions

Abstract

We study self-avoiding walks on critical percolation clusters by means of a recently developed exact enumeration method, which can handle walks of several thousand steps. We had previously presented results for the two- and three-dimensional cases; here we take a wider perspective and vary the system’s dimensions up to D = 7, beyond the supposed upper critical dimension of . These results may serve to check analytical predictions and help understand how the medium’s fractal structure impacts on the walks’ scaling behavior.