Abstract
We carry out the first exact enumeration studies of random walks on the percolation backbone. Using a relation between the backbone and the full cluster, we find for the conductivity exponent , which means that the Alexander-Orbach conjecture for percolation can hold only if our error bars were multiplied by a factor of 3. We also perform the first calculations of the chemical length exponent that measures the dependence on of the number of backbone sites within a chemical distance ; we find .
- Received 10 February 1984
DOI:https://doi.org/10.1103/PhysRevB.30.4083
©1984 American Physical Society