Percolation Theory of Nonlinear Circuit Elements

Percolation theory is extended to the case of circuit elements with nonlinear I-V characteristics, particularly the special cases V=I^αr, which form the universality classes. Near the percolation threshold the "conductance" IV^1α vanishes like (p-pc)ᵗ, where t depends on α and dimensionality. The Skal-Shklovskii-De Gennes model gives t(α)=(d-1)ν+(φ-ν)α, where φ is only weakly dependent on α and d, and approaches unity at $d=6$. Renormalization methods are used to study the α dependence of t in two dimensions.