Hopping percolation transition in granular ferromagnets

We present computer simulations of the magnetotransport properties of two-dimensional and three-dimensional granular ferromagnets using a random resistor network in which the conductivity, σ, between pairs of neighboring grains depends upon the intergrain distance [σαexp (-κr), where κ is a measure of disorder and r is a random number, 0≤r≤1] and the relative magnetic orientations. We study the resistance (R) distribution function, P (R), and find that in both the weak disorder regime L κμ >1 (not sensitive to the removal of any single bond) and the strong disorder regime L κμ <1 (very sensitive to such a removal) the distribution depends only on L κμ and can be well approximated by a log-normal function with dispersion b κμ L, where b is a coefficient which depends on the type of the lattice and μ is the critical exponent of the percolation correlation length.