Abstract
The author investigates the scaling behaviour of the current distribution in the random resistor network at the percolation threshold under a weak magnetic field. A self-dual fractal model is used to mimic the two-dimensional percolation cluster at the threshold. The infinite set of exponents is calculated for the moments of the Ohmic and Hall current distribution on the regular fractal. The dependence of the multifractality on the magnetic field by the Hall effect is shown. It is found that the Ohmic and Hall current distribution shows a characteristic multifractality under a magnetic field.
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