Low-field Hall effect near the percolation threshold

We use a random-resistor-network model to study the critical behavior of the low-field Hall constant in a three-dimensional (3D) metal-insulator composite near the percolation threshold. The transfer-matrix method, which was originally introduced for calculating conductivity, is generalized to be applicable to the calculation of the Hall constant and the magnetoresistance as well. We then use this generalized method to perform a renormalization-group calculation for a cubic random resistor network and two simulations of random resistor networks at the percolation threshold: one of cubes and the other of long (3D) strips. Fitting an expression RH (p-pc)-g to the effective Hall constant RH of the network, we find a divergent Hall constant both from the renormalization-group calculation (g=0.625) and from the simulation of cubes (g=0.25), while the long-strips simulation yields one that is concentration independent, i.e., g=0.