TY - JOUR
T1 - Breakdown of Alexander-Orbach conjecture for percolation
T2 - Exact enumeration of random walks on percolation backbones
AU - Hong, Daniel C.
AU - Havlin, Shlomo
AU - Herrmann, Hans J.
AU - Stanley, H. Eugene
PY - 1984
Y1 - 1984
N2 - We carry out the first exact enumeration studies of random walks on the percolation backbone. Using a relation between the backbone and the full cluster, we find for the d=2 conductivity exponent t =0.970 0.009, which means that the Alexander-Orbach conjecture for percolation can hold only if our error bars were multiplied by a factor of 3. We also perform the first calculations of the chemical length exponent d l that measures the dependence on l of the number of backbone sites within a chemical distance l; we find d l=1.44 0.03.
AB - We carry out the first exact enumeration studies of random walks on the percolation backbone. Using a relation between the backbone and the full cluster, we find for the d=2 conductivity exponent t =0.970 0.009, which means that the Alexander-Orbach conjecture for percolation can hold only if our error bars were multiplied by a factor of 3. We also perform the first calculations of the chemical length exponent d l that measures the dependence on l of the number of backbone sites within a chemical distance l; we find d l=1.44 0.03.
UR - https://www.scopus.com/pages/publications/0001394810
U2 - 10.1103/physrevb.30.4083
DO - 10.1103/physrevb.30.4083
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AN - SCOPUS:0001394810
SN - 0163-1829
VL - 30
SP - 4083
EP - 4086
JO - Physical Review B-Condensed Matter
JF - Physical Review B-Condensed Matter
IS - 7
ER -