Abstract
We study the generalized resistive susceptibility, χ(λ)≡[exp[-1/2R(xx’)] where [ denotes an average over all configurations of clusters with weight appropriate to bond percolation, R(x,x’) is the resistance between nodes x and x’ when occupied bonds are assigned unit resistance and vacant bonds infinite resistance. For bond concentration p near the percolation threshold at , we give a simple calculation in 6-ε dimensions of χ(λ) from which we obtain the distribution of resistances between two randomly chosen terminals. From χ(λ) we also obtain the qth-order resistive susceptibility ≡[ν(x,x’) R(x,x’, where ν(x,x’) is an indicator function which is unity when sites x and x ’ are connected and is zero otherwise. In the latter case, ν(x,x ’)R(x,x ’ is interpreted to be zero. Our universal amplitude ratios, ≡ ((, reproduce previous results and agree beautifully with our new low-concentration series results. We give a simple numerical approximation for the ’s in all dimensions. The relation of the scaling function for χ(λ) with that for the susceptibility of the diluted xy model for p near is discussed.
- Received 11 July 1989
DOI:https://doi.org/10.1103/PhysRevB.41.4610
©1990 American Physical Society