Abstract
Current and logarithm-current distributions on a three-dimensional random-bond percolation cubic network were studied at the percolation threshold by computer simulations. Predictions of a hierarchical model that combine fractal structure and randomness agree with our numerical simulations. In the thermodynamic limit the logarithm-current distribution exhibits ann(ln(i))∼i 1/3 dependence below some characteristic currenti c. This distribution may scale with lni/lnL, but the data are insufficient to make this a definite conclusion. Due to the small range of lnL considered, a study of the moments does not reveal this behavior and a study of the distribution itself is required.
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Duering, E., Bergman, D.J. Current distribution on a three-dimensional, bond-diluted, random-resistor network at the percolation threshold. J Stat Phys 60, 363–381 (1990). https://doi.org/10.1007/BF01314926
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DOI: https://doi.org/10.1007/BF01314926