Yuval Gefen, Yoseph Imry, et al.
Surface Science
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. © 1980 The American Physical Society.
Yuval Gefen, Yoseph Imry, et al.
Surface Science
Benoit B. Mandelbrot
IEEE Transactions on Circuits and Systems
Benoit B. Mandelbrot, Yuval Gefen, et al.
Journal of Physics A: Mathematical and General
Simon Berger, M. Pechal, et al.
Nature Communications