Abstract
We show that for all Euclidean dimensions , where is the effective resistance between two points separated by a distance comparable with the correlation length is the fractal dimension of the backbone, and is the fractal dimension of a random walk on the same backbone. We also find a relation between the backbone and the full percolation cluster, . Thus the Alexander-Orbach conjecture ( for ) fails numerically for the backbone.
- Received 3 November 1983
DOI:https://doi.org/10.1103/PhysRevB.29.522
©1984 American Physical Society