Frequency dependent effective conductivity of two-dimensional metal-dielectric composites

We analyze a random resistor-inductor-capacitor $(RLC)$ lattice model of 2-dimensional metal-insulator composites. The results are compared with Bruggeman's and Landauer's Effective Medium Approximations where a discrepancy was observed for some frequency zones. Such a discrepancy is mainly caused by the strong conductivity fluctuations. Indeed, a two-branches distribution is observed for low frequencies. We show also by increasing the system size that at $p_c$ the so-called Drude peak vanishes; it increases for vanishing losses.