Critical phenomena on fractal lattices

Yuval Gefen*, Benoit B. Mandelbrot, Amnon Aharony

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

388 Scopus citations


Renormalization-group techniques are applied to Ising-model spins placed on the sites of several self-similar fractal lattices. The resulting critical properties are shown to vary with the (noninteger) fractal dimensionality D, but also with several topological factors: ramification, connectivity, lacunarity, etc. For any D>~1, there exist systems with both Tc=0, and Tc>0; hence a lower critical dimensionality is not defined. The nonvanishing values of Tc and the critical exponents depend on all these factors.

Original languageEnglish
Pages (from-to)855-858
Number of pages4
JournalPhysical Review Letters
Issue number11
StatePublished - 1980


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