TY - JOUR
T1 - Geometric implementation of hypercubic lattices with noninteger dimensionality by use of low lacunarity fractal lattices
AU - Gefen, Yuval
AU - Meir, Yigal
AU - Mandelbrot, Benoit B.
AU - Aharony, Amnon
PY - 1983
Y1 - 1983
N2 - It is claimed that the abstract analytic continuation of hypercubic lattices to noninteger dimensionalities can be implemented explicitly by certain fractal lattices of low lacunarity. These lattices are special examples of Sierpinski carpets. Their being of low lacunarity means that they are arbitrarily close to being translationally invariant. The claim is substantiated for the Ising model in D=1+ dimensions, and for resistor network models with 1<D<2.
AB - It is claimed that the abstract analytic continuation of hypercubic lattices to noninteger dimensionalities can be implemented explicitly by certain fractal lattices of low lacunarity. These lattices are special examples of Sierpinski carpets. Their being of low lacunarity means that they are arbitrarily close to being translationally invariant. The claim is substantiated for the Ising model in D=1+ dimensions, and for resistor network models with 1<D<2.
UR - http://www.scopus.com/inward/record.url?scp=0000439894&partnerID=8YFLogxK
U2 - 10.1103/PhysRevLett.50.145
DO - 10.1103/PhysRevLett.50.145
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AN - SCOPUS:0000439894
VL - 50
SP - 145
EP - 148
JO - Physical Review Letters
JF - Physical Review Letters
SN - 0031-9007
IS - 3
ER -