Angular structure of lacunarity, and the renormalization group
Ball, Robin, Caldarelli, Guido and Flammini, A.. (2000) Angular structure of lacunarity, and the renormalization group. Physical Review Letters, Vol.85 (No.24). pp. 5134-5137. ISSN 0031-9007Full text not available from this repository.
Official URL: http://dx.doi.org/10.1103/PhysRevLett.85.5134
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:||Journal Article|
|Subjects:||Q Science > QC Physics|
|Divisions:||Faculty of Science > Physics|
|Library of Congress Subject Headings (LCSH):||Fractals, Renormalization group|
|Journal or Publication Title:||Physical Review Letters|
|Publisher:||American Physical Society|
|Official Date:||11 December 2000|
|Number of Pages:||4|
|Page Range:||pp. 5134-5137|
|Funder:||Engineering and Physical Sciences Research Council (EPSRC), European Union (EU)|
|Grant number:||GR/L55346 (EPSRC), ERBFMBI-CT97-2746 (EU), FMRX-CT98-0183 (EU)|
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