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Angular structure of lacunarity, and the renormalization group

By Robin C. Ball, Guido Caldarelli and Alessandro Flammini

Abstract

We formulate the angular structure of lacunarity in fractals, in terms of a symmetry reduction of the three point correlation function. This provides a rich probe of universality, and first measurements yield new evidence in support of the equivalence between self-avoiding walks (SAW's) and percolation perimeters in two dimensions. We argue that the lacunarity reveals much of the renormalization group in real space. This is supported by exact calculations for random walks and measured data for percolation clusters and SAW's. Relationships follow between exponents governing inward and outward propagating perturbations, and we also find a very general test for the contribution of long-range interactions

Topics: QC Physics
Publisher: American Physical Society
Year: 2000
DOI identifier: 10.1103/PhysRevLett.85.5134
OAI identifier: oai:eprints.imtlucca.it:1160

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