Abstract
We investigate the sample-to-sample fluctuations in the conductivity of a random resistor network—equivalently, in the diffusivity of a disordered medium with symmetric hopping rates. We argue that whenever the effective conductivityσ * is strictly positive, then the fluctuations are normal, i.e., proportional to (volume)−1/2. If the local conductivities are allowed to be zero, thenσ * vanishes when approaching the percolation thresholdp c. Close top c the fluctuations are anomalous. From the renormalization group on hierarchical lattices we find that atp c fluctuations and mean scale in the same fashion, i.e., there is no independent scaling exponent for the fluctuations.
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Schlösser, T., Spohn, H. Sample-to-sample fluctuations in the conductivity of a disordered medium. J Stat Phys 69, 955–967 (1992). https://doi.org/10.1007/BF01058757
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DOI: https://doi.org/10.1007/BF01058757