The resistive susceptibility of random diode-insulator networks

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Abstract
The authors consider regular crystal lattices in which the bonds are either diodes (probability p) or insulators. The mean number of backbone bonds LBB(p) when averaged over lattice points is found to be related to the mean size of clusters S(p) by LBB(p)=zpS(p) where z is the number of bonds directed away from any lattice site. Thus LBB diverges at pc with the mean size exponent gamma . The resistive susceptibility chi R(p) of Harris and Fisch (1977, 1978) is expanded graphically as a power series in p and it is found that term by term chi R(p)= Psi R(p)(S(p))2 where Psi R(p) is obtained from chi R(p) by ignoring contributions from nodal graphs. The above results are valid for bond and site dilution in any dimension. For bond dilution on the square lattice the authors have determined Psi R(p) to p17 and Pade analysis of the resulting series for chi R(p) shows that it diverges with exponent gamma R=3.654+or-0.017. Using a scaling relation the exponent t for the conductivity of the infinite cluster is estimated to be t=0.75+or-0.02.

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