Criticality in non-linear transport properties of heterogeneous materials

In heterogeneous materials consisting of individual simple non-linear elements whose transport characteristics are piecewise linear separated by random « thresholds », one may encounter transition regimes where a power law relates fluxes to potentials. There is a well-defined threshold for the onset of this transition regime. We suggest that this threshold is a critical point closely related to the percolation one. We study numerically the value of the threshold by different means, in a directed and a isotropic case, and obtain estimates through finite-size scaling.