Conductance and resistance jumps in finite-size random resistor networks

Publisher Website
Google Scholar
Abstract
When bonds are removed one by one and at random from a finite-size resistor network, the conductance (or resistance) does not change continuously, but rather a sequence of conductance (resistance) jumps for various sizes occurs. The larger jumps arise from those bonds which carry a relatively large current just before they are cut. The authors report on numerical simulations of these jumps of a random resistor network on the square lattice. They also give a scaling argument to account for this phenomenon, which yields the number of conductance jumps larger than Delta G scaling as ( Delta G)- lambda (G), with lambda (G) =d nu /(d nu -t), where t is the conductivity exponent and nu is the percolation correlation-length exponent. Equivalently, the number of resistance jumps greater than Delta R scales as ( Delta R)- lambda (R), with lambda (R)=d nu /(d nu +t). These predictions account for the data on a qualitative level only, however, and they discuss some possible mechanisms for the quantitative discrepancies.