Exact series studies of self-avoiding walks on two-dimensional critical percolation clusters

Abstract

The author presents results of exact series studies of self-avoiding walks on percolation clusters on the square lattice performed very close to the percolation threshold and estimates the critical exponents nu and gamma defined by the disorder averages of the mean square radius of gyration or the end-to-end distance and the number of self-avoiding walks, respectively. The self-avoiding walk configurations are enumerated exactly up to 35 steps. The result for nu indicates a large increase compared with the self-avoiding walks on fully occupied lattice. The result for gamma , however, indicates a behaviour similar to that on a fully occupied lattice. The result for nu is completely different from that of Lee, Nakanishi and Kim (1989).