Angular structure of lacunarity, and the renormalization group

Ball, Robin C. and Caldarelli, Guido and Flammini, Alessandro Angular structure of lacunarity, and the renormalization group. Physical Review Letters, 85 (24). pp. 5134-5137. ISSN 0031-9007 (2000)

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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.

Item Type:	Article
Identification Number:	https://doi.org/10.1103/PhysRevLett.85.5134
Additional Information:	© 2000 American Physical Society
Uncontrolled Keywords:	PACS: 64.60.Ak, 05.40.Fb
Subjects:	Q Science > QC Physics
Research Area:	Economics and Institutional Change
Depositing User:	Ms T. Iannizzi
Date Deposited:	23 Feb 2012 11:26
Last Modified:	05 Dec 2014 09:35
URI:	http://eprints.imtlucca.it/id/eprint/1160

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