Percolation Characteristics in Discontinuous Thin Films of Pb

The geometrical features of discontinuous Pb films are analyzed in terms of the scaling theory of percolation. Above the percolation threshold it is shown that the infinite cluster as well as the backbone has an anomalous mass distribution up to a length of the order of the percolation correlation length (${\ensuremath{\xi}}_{p}$), corresponding to that of self-similar objects. Above ${\ensuremath{\xi}}_{p}$, the mass distribution is homogeneous. Below the percolation threshold, the cluster statistics agrees with scaling theory.