Percolation theory for nonlinear conductors

Under broad conditions, a network of nonlinear conductors has an I-V characteristic uniquely determined by Kirchhoff's rules. By means of a renormalization calculation, we show that near the percolation threshold the details of the microscopic I-V characteristic are averaged out, so that the bulk material approaches power-law conductor behavior (V=I±). The threshold exponents t(±) and s(±) are discussed in the limiting cases of two dimensions (where they are related by duality) and high dimensionality (by solving the Cayley-tree model).