Solvable fractal family, and its possible relation to the backbone at percolation

Yuval Gefen, Amnon Aharony, Benoit B. Mandelbrot, Scott Kirkpatrick

Research output: Contribution to journalArticlepeer-review

320 Scopus citations

Abstract

A nontrivial family of d-dimensional scale-invariant fractal lattices is described, on which statistical mechanics and conductivity problems are exactly solvable for every d. These fractals are finitely ramified but not quasi one dimensional, and hence can be used to model the important geometrical features of the percolating cluster's backbone. Critical exponents calculated for this model agree with those of "real" systems at low dimensionalities.

Original languageEnglish
Pages (from-to)1771-1774
Number of pages4
JournalPhysical Review Letters
Volume47
Issue number25
DOIs
StatePublished - 1 Jan 1981
Externally publishedYes

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