Flicker (1f) Noise in Percolation Networks: A New Hierarchy of Exponents

Abstract

New results for the magnitude of flicker noise, considered as resistance fluctuations, in random resistor networks are reported. Near the percolation threshold p c , the magnitude of the relative noise is shown to diverge as (p-p c )~K. The new exponent K is calculated by various methods: Monte Carlo simulations, effective-medium theory, and position-space renormalization group. Exponents pertaining to higher-order cumulants of the resistance fluctuations are also calculated. The possible implications of our results for ongoing experiments on metal-insulator mixtures and cermets are also discussed.

Anomalous scaling laws in multifractal objects

“…The critical behaviour of random resistor networks is a percolation problem which can be studied by means of the multifractal approach [ARC85, RTBT85].…”

Multifractal properties of resistor diode percolation

“…Since the 1980s several publications have appeared that have addressed multifractality in IP by studying random resistor networks (RRNs) [19,20,21,22,23,24,25]. A RRN is a simple bond percolation model on a ddimensional hypercubic lattice where bonds between nearest neighboring sites are occupied with probability p with a resistor or empty with probability 1 − p. In a typical setup one has two leads positioned at two connected lattice sites x and x ′ at which a fixed external current I is injected and, respectively, extracted.…”

Magnetically driven electronic phase separation in the semimetallic ferromagnet EuB6

“…In general, diverging 1/f -type resistance (or conductance) fluctuations are typical for percolative metalinsulator transitions [27,28]. In a classical percolation scenario, the resistance and resistance noise, respectively, are expected to scale as R, S R /R 2 ∝ (p − p c ) −t,κ .…”