Geometric implementation of hypercubic lattices with noninteger dimensionality by use of low lacunarity fractal lattices

Yuval Gefen; Yigal Meir; Benoit B. Mandelbrot; Amnon Aharony

doi:10.1103/PhysRevLett.50.145

Geometric implementation of hypercubic lattices with noninteger dimensionality by use of low lacunarity fractal lattices

Yuval Gefen, Yigal Meir, Benoit B. Mandelbrot, Amnon Aharony

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222 Scopus citations

Abstract

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.

Original language	English
Pages (from-to)	145-148
Number of pages	4
Journal	Physical Review Letters
Volume	50
Issue number	3
DOIs	https://doi.org/10.1103/PhysRevLett.50.145
State	Published - 1 Jan 1983
Externally published	Yes

ASJC Scopus subject areas

General Physics and Astronomy

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Geometric implementation of hypercubic lattices with noninteger dimensionality by use of low lacunarity fractal lattices

Abstract

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