Abstract
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 , but also with several topological factors: ramification, connectivity, lacunarity, etc. For any , there exist systems with both , and ; hence a lower critical dimensionality is not defined. The nonvanishing values of and the critical exponents depend on all these factors.
- Received 12 May 1980
DOI:https://doi.org/10.1103/PhysRevLett.45.855
©1980 American Physical Society