What is the relevant length scale when studying percolating clusters: a critical study

Percolation clusters are known to be well described by the percolation correlation length ξ. In fact, this length is defined by the geometry of the clusters, and thus can only give an account of zero frequency (time independent) physical properties, such as dc conductivity or fractal morphology of 2D or 3D clusters. Taking examples on optical properties of granular metal films close to the percolation threshold, we show that the relevant length scale L is not known well. It depends explicitly on the kind of measurement, and on the frequency ω at which the physical properties are observed. We conclude that, in the region where L(ω)<ξ, only a scaling model can give a full account of the experimental results, and that, in the region where L(ω)>ξ, an averaged beheviour can also be used.