TY - JOUR
T1 - Critical phenomena on fractal lattices
AU - Gefen, Yuval
AU - Mandelbrot, Benoit B.
AU - Aharony, Amnon
PY - 1980
Y1 - 1980
N2 - 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.
AB - 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.
UR - http://www.scopus.com/inward/record.url?scp=0000386107&partnerID=8YFLogxK
U2 - 10.1103/PhysRevLett.45.855
DO - 10.1103/PhysRevLett.45.855
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AN - SCOPUS:0000386107
SN - 0031-9007
VL - 45
SP - 855
EP - 858
JO - Physical Review Letters
JF - Physical Review Letters
IS - 11
ER -