Abstract
A model, based on the Kadanoff 's block method, has been developed for the calculation of an effective function (D.F.) for a 2D thin island film. This model takes into account: (i) the real morphology of the films, which is the main parameter near the percolation threshold, (ii) the interactions at any range using a renormalization process. At each step of this process, the D.F. is calculated using a 2D theory and no free parameter is introduced. This model is valid at any metal concentration and predicts, as applied to a simulated random lattice the dielectric resonance and the percolation. The calculated effective D.F. is found to obey scaling laws with critical exponents s 2D=1.35 for the effective polarization and t 2D=1.52 for the conductivity, very close to the theoretical 2D estimates ( s=1.35, t=1.35).
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