Abstract
We have found from numerical simulation that the minimum current in the two-component random resistor network at criticality scales anomalously with the ratio h of poor to good conductances: (h)≊exp[-const×(lnh]. Exact analytic calculations in the diamond fractal confirm the result. In addition, we obtain a crossover behavior (h)/(1)=exp[-const×(lnh]H(), where L is the size of the network, H is a function describing the crossover from fractal to homogeneous behaviors, and φ is the crossover exponent. The exponential prefactor is analogous to the behavior of left-sided multifractality in diffusion-limited aggregations.
- Received 3 August 1992
DOI:https://doi.org/10.1103/PhysRevB.46.12137
©1992 American Physical Society