Topology of a two-component disordered system below and above the percolation threshold

Abstract The influence of geometry of a two-component system composed of randomly distributed metal and dielectric regions on various kinetic coefficients (conductivity, Hall effect in a weak magnetic field, thermoelectric power) is studied near the percolation threshold. Rigorous mathematical theorems for the conductivity and Hall effect in the critical regimes are stated. A new correlation length, called here the infinite-cluster macrobond length, is defined and its critical exponent calculated to be a(p) α δp −g at p → pc + 0, where g = 1.4 ± 0.1 in 2-D space and g = 0.98 ± 0.1 in 3-D space.