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Phase transition in the topological properties of the generalized percolation model

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  • Djordjevic, Zorica V.

Abstract

Within the generalized percolation model we study scaling behavior of the cluster-size- chemical-distance distribution function gsl, 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 gsl function, with exp(−l) taken as a fractal measure, for k<0, exhibit multifractal behavior with an exponential dependence on s. At k=0 the same analysis indicates the occurence of a phase transition in the spectrum of multifractal exponents. For k > 0, gsl 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.

Suggested Citation

  • Djordjevic, Zorica V., 1992. "Phase transition in the topological properties of the generalized percolation model," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 187(3), pages 425-435.
    • Handle: RePEc:eee:phsmap:v:187:y:1992:i:3:p:425-435
    DOI: 10.1016/0378-4371(92)90003-9
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