Double universality of 1/f noise percolation-like exponent in systems with exponentially wide spectrum of resistances

Theory and numerical simulations of /1f noise in random networks in which bonds take resistance r ∼ exp(-λx), where x is a random variable and λ ⪢ are presented. For microscopic noise generating mechanism which obeys the form of {δr2} ∼ r2+θ, it is shown that the overall noise intensity of the network is given by Ce ∼ λm exp(-λθxc), where 1 − xc is the percolation threshold. In the range 0 ⩽ θ < 2 exponent m is “double universal”, i.e. it is independent of the lattice geometry and of microscopic noise generating mechanism. Numerical simulations give m ≌ 2.5.