PHASE-TRANSITION IN THE TOPOLOGICAL PROPERTIES OF THE GENERALIZED PERCOLATION MODEL

Within the generalized percolation model we study scaling behavior of the cluster-size-chemical-distance distribution function g(sl), specifying the number of clusters of mass s and chemical distance l. Using the exact series analysis we show that the kth moments of the g(sl) function, with exp(-l) taken as a fractal measure, for k < 0. exhibit muitifractal behavior with an exponential dependence on s. At k = 0 the same analysis indicates the occurrence of a phase transition in the spectrum of multifractal exponents. For k > 0, g(sl), possesses a power law dependence on s with a constant gap exponent, which agrees with previous results for the mass-chemical-distance probability distribution function and the mean chemical distance of the percolation clusters and lattice animals.