Scaling theory of the low-field Hall effect and magnetoresistance near a percolation threshold

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Abstract
The scaling theory of the low-magnetic-field Hall effect in a metal-non-metal mixture near its percolation threshold is reviewed and extended to discuss the magnetoresistance in low fields. It is shown that different types of critical behaviour are possible for the Hall coefficient and for the relative magnetoresistance of the mixture, depending upon the physical parameters of the mixture. A pair of new exponents are introduced to describe the critical behaviour of the second-order Hall contribution to the magnetoresistance of the mixture, and upper and lower bounds are suggested for their values.