Conductivity anisotropy and the Hall effect in inhomogeneous conductors near the percolation threshold

Near the percolation threshold the off-diagonal elements of the conductivity tensor (which describe the conductivity anisotropy and the Hall effect) vanish faster than the conductivity itself. The Cayley tree model is generalised to describe this effect, and the exponents which characterise the various anisotropies are found. The results disagree with the high-dimensionality limits of the various exponent relationships that have been previously proposed by Shklovskii (1978) and by Levinshtein et al. (1976). The special case of the Hall effect in two dimensions is also discussed.