TY - JOUR

T1 - Low-field Hall effect near the percolation threshold

AU - Marianer, S.

AU - Bergman, D. J.

PY - 1989

Y1 - 1989

N2 - 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.

AB - 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.

UR - http://www.scopus.com/inward/record.url?scp=35949013229&partnerID=8YFLogxK

U2 - 10.1103/PhysRevB.39.11900

DO - 10.1103/PhysRevB.39.11900

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AN - SCOPUS:35949013229

SN - 0163-1829

VL - 39

SP - 11900

EP - 11906

JO - Physical Review B-Condensed Matter

JF - Physical Review B-Condensed Matter

IS - 16

ER -