Anomalous crossover behaviors in the two-component random resistor network

Abstract

It has been found from numerical simulation that the minimum current in the two-component random resistor network at percolation scales anomalously with the ratio h of poor to good conductances, I min( h)≈exp(−constant × (ln h) 2). Exact analytic calculations in the hierarchical diamond lattice confirm the result. The exponential prefactor is analogous to the behavior of left-sided multifractality in diffusion limited aggregations.