Monte Carlo study of self-avoiding walks on a critical percolation cluster

We present the results of Monte Carlo simulation for self-avoiding walks on a percolation cluster for square and simple cubic lattices performed very close to the percolation thresholds and estimate critical exponents {ν} and {γ} defined by the disorder averages of the mean-square radius of gyration and the number of self-avoiding walks, respectively. Our results for {ν} indicate a behavior rather similar to the self-avoiding walks on fully occupied lattice unlike the large increase in {ν} reported in the only previous work of this kind by Kremer given for the diamond lattice. Our results for {γ} suggest an increase from the full lattice value just at pc in three dimensions, while in two dimensions the asymptotic behavior appears to be similar to that of the ordinary self-avoiding walks. We also consider the possible crossover from fractal to Euclidean behavior and discuss the reasons why no crossover scaling is observed for the mean-square radius of gyration in the present calculation.