Statistical and scaling properties of the alternating-current conductivityin thin metal-dielectric composites

We study in this paper the scaling and statistical properties of the altern ating-current conductivity of thin metal-dielectric composite films for dif ferent degrees of loss in metallic components and particularly in the limit of vanishing losses. We model the system as a two-dimensional RLC network and calculate the effective conductivity by using a real-space renormalizat ion group method. It is found that the real conductivity fluctuates strongl y for very small losses. The correlation length diverges for vanishing loss es leading to the failure of the effective-medium theory to describe the di electric properties of such systems in this limit. We found also that the d istribution of the real conductivity becomes log-normal below a certain cri tical loss R-c which is size dependent for finite systems. There is further discussion on the statistical characterization of the optical modes.