Abstract
The bulk conductivity (p) of the bond lattice in with a fraction p of conducting bonds is analyzed. Assuming a hierarchical node-link-blob (NLB) model of the conducting backbone, it is shown that (p) (for this model) is convex in p near the percolation threshold , and that its critical exponent t obeys the inequalities 1≤t≤2 for d=2,3, while 2≤t≤3 for d≥4. The upper bound t=2 in d=3, which is realizable in the NLB class, virtually coincides with two very recent numerical estimates obtained from simulation and series expansion.
- Received 18 June 1990
DOI:https://doi.org/10.1103/PhysRevLett.65.2923
©1990 American Physical Society