Abstract
We study the complex admittance (ac conductivity and dielectric constant) of conductor-insulator composite material, based on a two-dimensional square network consisting of randomly placed conductors and capacitors. We derived some exact analytical relations between the complex admittances of high and low frequencies and of complementary conductor concentrations. We calculate the complex admittance by applying a transfer-matrix method to a square network and study the dependence on both the frequency and the conductor concentration. The numerical results are compared with an effective-medium theory, and the range of applicability and limitation of the effective-medium theory are clarified.
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