MONTE-CARLO STUDY OF SELF-AVOIDING WALKS ON A PERCOLATION CLUSTER

We present computer-simulation results of self-avoiding walks (SAW's) on a percolation cluster for a square lattice performed very close to the percolation threshold. We specifically consider the disorder averages of SAW's on all clusters supporting one or more N-step walks and those on a backbone of an infinite cluster and estimate the critical exponents-nu and gamma that characterize the disorder averages of the end-to-end distance and the number of SAW's, respectively. Our results for gamma indicate a behavior rather similar to SAW's on fully occupied lattices for both cases, while for nu one of two cases shows different behavior.