Critical Phenomena on Fractal Lattices

著者: Yuval Gefen, Benoît B. Mandelbrot, Amnon Aharony - Physical Review Letters 1980 被引用: 450

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 ${T}_{c}=0$, and ${T}_{c}>0$; hence a lower critical dimensionality is not defined. The nonvanishing values of ${T}_{c}$ and the critical exponents depend on all these factors.