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A Mixed-Transfer-Matrix Method for Simulating Normal Conductor/Perfect Insulator/Perfect Conductor Random Networks

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Abstract

We develop a mixed-transfer-matrix approach for computing the macroscopic conductivity of a three-constituent normal conductor/perfect insulator/perfect conductor random network. This is applied to two-dimensional and three-dimensional samples at a percolation threshold. Such networks are simulated in order to test whether a diluted percolating network of normal conducting bonds remains in the same universality class of critical behavior when a finite fraction of those bonds have been replaced by perfectly conducting bonds. Also tested by such simulations is whether a percolating mixture of normal and perfectly conducting bonds remains in the same universality class of critical behavior when a finite fraction of the normal bonds are replaced by perfectly insulating bonds. These questions are crucial for some recently published exact results which connect the macroscopic electrical and elastic responses of percolating networks.

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Authors and Affiliations

  1. School of Physics and Astronomy, Raymond and Beverly Sackler Faculty of Exact Sciences, Tel Aviv University, Israel;

    Xiangting Li & David J. Bergman

  2. Institute of Theoretical Physics, Shanghai Jiaotong University, People's Republic of China

    Xiangting Li

Authors
  1. Xiangting Li
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  2. David J. Bergman
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Li, X., Bergman, D.J. A Mixed-Transfer-Matrix Method for Simulating Normal Conductor/Perfect Insulator/Perfect Conductor Random Networks. Journal of Statistical Physics 117, 427–452 (2004). https://doi.org/10.1007/s10955-004-2272-x

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  • DOI: https://doi.org/10.1007/s10955-004-2272-x

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