Percolation transition in a two-dimensional system of Ni granular ferromagnets

We model magnetotransport features of the quenched condensed granular Ni thin films by a random two-dimensional resistor network in order to test the condition where a single bond dominates the system. The hopping conductivity is assumed to depend on the distance between neighboring ferromagnetic grains and the mutual orientation of the magnetic moments of these grains. We find that the quantity characterizing the transition from weak disorder (not sensitive to a change of a single bond resistivity) to strong disorder (very sensitive to such changes) scales as $\kappa ∕L^{1∕1.3}$, where $L$ is the size of the system and $\kappa$ is a measure of disorder.