TY - JOUR

T1 - Series analysis of randomly diluted nonlinear networks with negative nonlinearity exponent

AU - Meir, Yigal

AU - Blumenfeld, Raphael

AU - Harris, A. Brooks

AU - Aharony, Amnon

PY - 1987/1/1

Y1 - 1987/1/1

N2 - The behavior of randomly diluted networks of nonlinear resistors, for each of which the voltage-current relationship is |V|=r|I|±, where ± is negative, is studied using low-concentration series expansions on d-dimensional hypercubic lattices. The average nonlinear resistance R between a pair of points on the same cluster, a distance r apart, scales as r(±), where is the correlation-length exponent for percolation, and we have estimated (±) in the range -1±0 for 1d6. (±) is discontinuous at ±=0 but, for ±<0, (±) is shown to vary continuously from max, which describes the scaling of the maximal self-avoiding-walk length (for ±'0-), to BB, which describes the scaling of the backbone (at ±=-1). As ± becomes large and negative, the loops play a more important role, and our series results are less conclusive.

AB - The behavior of randomly diluted networks of nonlinear resistors, for each of which the voltage-current relationship is |V|=r|I|±, where ± is negative, is studied using low-concentration series expansions on d-dimensional hypercubic lattices. The average nonlinear resistance R between a pair of points on the same cluster, a distance r apart, scales as r(±), where is the correlation-length exponent for percolation, and we have estimated (±) in the range -1±0 for 1d6. (±) is discontinuous at ±=0 but, for ±<0, (±) is shown to vary continuously from max, which describes the scaling of the maximal self-avoiding-walk length (for ±'0-), to BB, which describes the scaling of the backbone (at ±=-1). As ± becomes large and negative, the loops play a more important role, and our series results are less conclusive.

UR - http://www.scopus.com/inward/record.url?scp=0042975228&partnerID=8YFLogxK

U2 - 10.1103/PhysRevB.36.3950

DO - 10.1103/PhysRevB.36.3950

M3 - Article

AN - SCOPUS:0042975228

SN - 0163-1829

VL - 36

SP - 3950

EP - 3952

JO - Physical Review B

JF - Physical Review B

IS - 7

ER -