AC properties of 2D percolation networks: a transfer matrix approach

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Abstract
The frequency dependent AC properties of 2D random resistor-capacitor mixtures are studied through a numerical transfer matrix method. The algorithm, which generalises to the complex impedances used by Herrmann et al. (1984) permits a detailed study of the scaling laws obeyed by the complex dielectric constant in the critical regime (low frequency and concentration close to the geometrical percolation threshold). The duality property of the system is extensively used throughout the analysis. Quantities of experimental interest, such as the loss angle delta and the Cole and Cole plot of the dielectric constant, are also examined, both close to and away from the critical point.