Anomalous crossover behaviours in the two-component deterministic percolation model

Abstract

The authors have investigated the current distribution in the two-component deterministic percolation model in which the ratio h of poor to good conductance is regarded as a small parameter. It is found that the minimum current Imin(h) scales anomalously with h: Imin(h)/Imin(1)=exp(-constant(ln h)2)H(hLphi ), where L is the size of the network, H a function describing the crossover from fractal to homogeneous behaviours and phi the crossover exponent. The exponential prefactor is quite similar to the behaviour of left-sided multifractality in diffusion limited aggregations. It is found that phi coincides with the crossover exponent for all multifractal moments of the current distribution.