Self-dual fractal models for the low-field Hall effect near percolation threshold

Abstract

Fractal lattices with the 'self-duality' property are proposed to imitate the geometric texture of two-dimensional percolating networks at percolation threshold. The exponents describing the power law dependence on the scale length of the Hall and Ohmic conductivities are found. The exponent for the Hall conductivity agrees with twice that for the Ohmic conductivity. The model is extended to describe the approach towards the threshold. It is found that the model shows the typical percolation behaviour as a function of a parameter p (the bond concentration).