We calculate the average number of steps N for edge-to-edge, "normal," and indefinitely growing self-avoiding walks (SAWs) on two-dimensional critical percolation clusters, using the real-space renormalization-group approach, with small "H" cells. Our results are of the form N = ALDSAW + B, where L is the end-to-end distance. Similarly to several deterministic fractals, the fractal dimensions DSAW for these three different kinds of SAWs are found to be equal, and the differences between them appear in the amplitudes A and in the correction terms B. This behavior is attributed to the hierarchical nature of the critical percolation cluster.
- Corrections to scaling
- Indefinitely growing self-avoiding walks
- Percolation clusters
- Real-space renormalization group
- Self-avoiding walks