Multifractality on Percolation Clusters

  • Amnon Aharony
Part of the NATO ASI Series book series (volume 167)


Following the introduction of fractals into statistical physics some six years ago,1 fractals became a growing active discipline in physics research. It has become clear that, at least over some range of length scales, many physical structures exhibit fractal geometry.2 Research has then divided into two main directions: First, attempts have been made to understand the physical mechanisms which govern the growth of structures (e.g. aggregates) into their particular fractal shapes.3,4,5 As recently commented by Kadanoff,6 there remain many open questions to be studied in this direction. In the second direction, the fractal geometry is taken as given, and the physical properties of the structure are then studied. Different physical properties turn out to be determined by subsets of sites (or bonds, or particles) on the structure, each having its own fractal nature. At the present time several infinite sets of independent fractal dimensionalities, or critical exponents, have been identified and studied. This paper aims to review this plenitude of exponents. Although the paper does not specifically discuss dynamics, many of the concepts introduced here are also used to describe dynamic phenomena, e.g. random walks, waves and breakdown phenomena. This lecture is meant to serve as an introduction to those subjects.


Fractal Geometry Percolation Cluster Fractal Dimensionality Small Current Kirchhoff Equation 
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Copyright information

© Plenum Press, New York 1987

Authors and Affiliations

  • Amnon Aharony
    • 1
  1. 1.School of Physics and AstronomyTel Aviv UniversityTel AvivIsrael

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