TY - JOUR

T1 - Critical behavior of the Hall effect near the percolation threshold using a new network model

AU - Duering, Edgardo

AU - Bergman, David J.

N1 - Funding Information:
This researchw as supportedi n part by the U.S.-Israel Binational Science Foundation under Grant 354/85a nd by a grant from the Center of Absorption in Science.

PY - 1989/5/1

Y1 - 1989/5/1

N2 - Electrical properties of metal-insulator composites are described by power law behavior when the concentration of metal p approaches the percolation threshold pc. The conductivity σ, the Hall conductivity λ, and the Hall coefficient R satisfy σ ∼(p - pc)t, λ ∼(p - pc)τ, R ∼(p - pc)-g. We develop a new three dimensional random resistor network model to obtain τ and g in which the nodes of the percolating backbone are the crucial elements producing the Hall effect. Finite size scaling ideas were applied near the effective percolation threshold pc(L), where L is the linear dimension of the system. We obtain g = 0.49 ± 0.06, τ = 3.56 ± 0.06 and t = 2.02 ± 0.06.

AB - Electrical properties of metal-insulator composites are described by power law behavior when the concentration of metal p approaches the percolation threshold pc. The conductivity σ, the Hall conductivity λ, and the Hall coefficient R satisfy σ ∼(p - pc)t, λ ∼(p - pc)τ, R ∼(p - pc)-g. We develop a new three dimensional random resistor network model to obtain τ and g in which the nodes of the percolating backbone are the crucial elements producing the Hall effect. Finite size scaling ideas were applied near the effective percolation threshold pc(L), where L is the linear dimension of the system. We obtain g = 0.49 ± 0.06, τ = 3.56 ± 0.06 and t = 2.02 ± 0.06.

UR - http://www.scopus.com/inward/record.url?scp=45149143185&partnerID=8YFLogxK

U2 - 10.1016/0378-4371(89)90286-0

DO - 10.1016/0378-4371(89)90286-0

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AN - SCOPUS:45149143185

SN - 0378-4371

VL - 157

SP - 125

EP - 129

JO - Physica A: Statistical Mechanics and its Applications

JF - Physica A: Statistical Mechanics and its Applications

IS - 1

ER -