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arXiv · 1401.3924

Crossover behavior of conductivity in a discontinuous percolation model

Seongmin Kim·Y. S. Cho·N. A. M. Araujo·B. Kahng
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Abstract

When conducting bonds are occupied randomly in a two-dimensional square lattice, the conductivity of the system increases continuously as the density of those conducting bonds exceeds the percolation threshold. Such a behavior is well known in percolation theory; however, the conductivity behavior has not been studied yet when the percolation transition is discontinuous. Here we investigate the conductivity behavior through a discontinuous percolation model evolving under a suppressive external bias. Using effective medium theory, we analytically calculate the conductivity behavior as a function of the density of conducting bonds. The conductivity function exhibits a crossover behavior from a drastically to a smoothly increasing function beyond the percolation threshold in the thermodynamic limit. The analytic expression fits well our simulation data.

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BibTeXRIS

Seongmin Kim, Y. S. Cho, N. A. M. Araujo, B. Kahng. 2014-01-16. Crossover behavior of conductivity in a discontinuous percolation model. https://doi.org/10.1103/physreve.89.032113

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