Angular Structure of Lacunarity, and the Renormalization Group

R. C. Ball, G. Caldarelli, and A. Flammini
Phys. Rev. Lett. 85, 5134 – Published 11 December 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.

  • Received 24 March 2000

DOI:https://doi.org/10.1103/PhysRevLett.85.5134

©2000 American Physical Society

Authors & Affiliations

R. C. Ball1, G. Caldarelli2,3, and A. Flammini1,2

  • 1Department of Physics, University of Warwick, CV4 7AL Coventry, United Kingdom
  • 2TCM Group, Cavendish Laboratory, University of Cambridge, CB3 0HE Cambridge, United Kingdom
  • 3INFM-Università di Roma 1 “La Sapienza,” Piazzale Aldo Moro 2, 00185 Roma, Italy

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Vol. 85, Iss. 24 — 11 December 2000

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