1/f noise in percolation and percolationlike systems

The behavior of 1/f noise effective intensity in two-phase percolation systems and percolationlike systems with an exponentially wide distribution of bond resistances is reviewed. Monte Carlo simulations on random resistor networks are performed. For a two-phase system the numerical values of noise critical exponents κ=1.54±0.025, κ′=0.61±0.02, w=6.31±0.25, and w′=6.9±0.25 are found in agreement with theoretical analysis performed with the help of a hierarchical model of a two-phase percolation system. For a system with an exponentially wide spectrum of bond resistances, i.e., a system in which bonds take on resistances r=r₀ exp(-λx), where λ≫1 and x is a random variable, it is assumed that in the individual resistors the noise generating mechanism obeys the form {δr²}∼r^2+θ. In this case the effective noise intensity C_e≡SΩ, where S is the relative power spectral density of system resistance fluctuations and Ω is the system volume, is given by C_e∼λ^m exp(-λθx_c), where 1-x_c is the percolation threshold. The exponent m is ‘‘double universal,’’ i.e., it is independent of lattice geometry and of the microscopic noise generating mechanism. Numerical simulations performed for θ=1 and 0 give approximately m≃2.3 and confirm this ‘‘double universality’’ of the exponent m. The connections between 1/f noise effective intensity and effective susceptibility in a two-phase weakly nonlinear percolation system are also established. © 1996 The American Physical Society.