A fractal model for the low-field Hall effect at three-dimensional percolation threshold

Abstract

A fractal model is proposed to determine the critical behaviour of the low-field Hall effect in a three-dimensional metal-non-metal composite at the percolation threshold. The fractal lattice is constructed to imitate the geometric texture of three-dimensional percolation clusters at criticality and to realise the Hall problem on a three-dimensional discrete lattice. The exponents describing the power law dependence on scale length of the Hall and ohmic conductivities are found.