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.
|Titolo:||Angular structure of lacunarity, and the renormalization group|
|Data di pubblicazione:||2000|
|Appare nelle tipologie:||1.1 Articolo in rivista|