Break-collapse method for resistor networks and a renormalisation-group application

Abstract
The break-collapse method recently introduced for the q-state Potts model is adapted for resistor networks. This method greatly simplifies the calculation of the conductance of an arbitrary two-terminal d-dimensional array of conductances, obviating the use of either Kirchhoff's laws or the star-triangle transformation. In addition, a real-space renormalisation group based on a new type of averaging gives excellent results for the conductivity of the random-resistor network on the square lattice.
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