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 {ν} and {γ} that characterize the disorder averages of the end-to-end distance and the number of SAW's, respectively. Our results for {γ} indicate a behavior rather similar to SAW's on fully occupied lattices for both cases, while for {ν} one of two cases shows different behavior.