Abstract
The question of transport in a random two-component mixture is addressed. To this end, two models are precisely formulated that effectively extend to two-component mixtures the de Gennes ant model of one-component systems. The authors develop and test a scaling theory, and solve some of the problems associated with the limit where one of the components is superconducting. The work provides the first practical realisation of the termite model of a random superconducting network, which performs a normal walk in the normal regions of the material but performs a new and unique form of random walk in the superconducting regions. They find that the divergence of the electrical conductivity at the percolation threshold can be described by this random walk, and that the critical exponent s is given by s=1.3+or-0.1 in d=2. If one perturbs away from the pure superconducting limit, they find that the electrical properties can still be describes by the random walk model, with a crossover exponent phi approximately=0.4 (d=2). Moreover, they find that the diffusion constant in this region is described by a scaling form, so that data can be made to collapse upon a single curve whose form is governed by the exponents s and phi .