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 $p_c$ 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.