TY - JOUR
T1 - AC response near the percolation threshold
T2 - Transfer-matrix results in two and three dimensions
AU - Bug, A. L.R.
AU - Grest, Gary S.
AU - Cohen, Morrel H.
AU - Webman, Itzhak
PY - 1987
Y1 - 1987
N2 - The complex admittivities of two- and three-dimensional networks of resistors and capacitors are calculated at pc using a transfer matrix. As predicted by scaling theories, the loss tangent becomes frequency independent in a critical range of frequencies. In three dimensions, for the usual model of unit conductors and capacitors at pc for the conductors, the dynamical exponents t and s are found to have values consistent with previous dc numerical studies. Similarly, the two-dimensional square site lattice and a bond lattice of superconductors and normal capacitors are both found to display dynamical scaling with universal (two-dimensional) exponents. Finally, two-dimensional networks with unit capacitors, but a power-law distribution of conductors, p()-± for ±<0 (and zero otherwise), are studied for the two cases ±=0 and 0.6. Dynamical scaling behavior is also seen on these lattices. In both cases, the bulk conductivities inferred from the dynamical scaling display nonuniversal values of the exponent t, while the exponent s remains at its universal value.
AB - The complex admittivities of two- and three-dimensional networks of resistors and capacitors are calculated at pc using a transfer matrix. As predicted by scaling theories, the loss tangent becomes frequency independent in a critical range of frequencies. In three dimensions, for the usual model of unit conductors and capacitors at pc for the conductors, the dynamical exponents t and s are found to have values consistent with previous dc numerical studies. Similarly, the two-dimensional square site lattice and a bond lattice of superconductors and normal capacitors are both found to display dynamical scaling with universal (two-dimensional) exponents. Finally, two-dimensional networks with unit capacitors, but a power-law distribution of conductors, p()-± for ±<0 (and zero otherwise), are studied for the two cases ±=0 and 0.6. Dynamical scaling behavior is also seen on these lattices. In both cases, the bulk conductivities inferred from the dynamical scaling display nonuniversal values of the exponent t, while the exponent s remains at its universal value.
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U2 - 10.1103/PhysRevB.36.3675
DO - 10.1103/PhysRevB.36.3675
M3 - Article
AN - SCOPUS:0011965409
SN - 0163-1829
VL - 36
SP - 3675
EP - 3682
JO - Physical Review B
JF - Physical Review B
IS - 7
ER -