Phase transitions on fractals. II. Sierpinski gaskets

Y. Gefen*, A. Aharony, Y. Shapir, B. B. Mandelbrot

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review


The authors construct and investigate a family of fractals which are generalisations of the Sierpinski gaskets (SGs) to all Euclidean dimensionalities. These fractal lattices have a finite order of ramification, and can be considered 'marginal' between one-dimensional and higher-dimensional geometries. Physical models defined on them are exactly solvable. The authors argue that short-range spin models on the SG show no finite-temperature phase transitions. As examples, they solve a few spin models and study the resistor network and percolation problems on these lattices.

Original languageEnglish
Article number028
Pages (from-to)435-444
Number of pages10
JournalJournal of Physics A: Mathematical and General
Issue number2
StatePublished - 1984


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