Critical Phenomena and Fractals with Dimensionality Near 1
This work is concerned with the critical properties of Ising models on self similar fractal lattices . Fractal lattices are not translationally invariant, in contrast to the usual integer dimensional lattices. A fractal’s simplest characteristic is its fractal dimensionality, D, which is ordinarily not an integer. (The ε-expansion arguments are predicated upon the existence of lattices that combine non integer dimensionality with translational invariance, but no such lattice has been actually exhibited). Numerous real physical systems, e.g. polymers and critical percolation clusters, are usefully viewed as self similar fractals [1,2].
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