Multifractality on Percolation Clusters

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