Asymptotic form of the spectral dimension at the fractal to lattice crossover
- 21 March 1988
- journal article
- editorial
- Published by IOP Publishing in Journal of Physics A: General Physics
- Vol. 21 (6) , 1477-1482
- https://doi.org/10.1088/0305-4470/21/6/024
Abstract
The authors study the spectral dimension of the Sierpinski gasket family of fractals. Each member of the family is labelled by an integer b(2S approximately=2-B/(1nb)beta , with B and beta being some constants. Here the authors demonstrate that this form should be replaced by the asymptotic law ds approximately=2-1n(1nb)+ constant/1nb. Their analysis is based on the exact calculation of the electric resistances Rb for all members of the family up to b=650.Keywords
This publication has 5 references indexed in Scilit:
- Asymptotic form of the spectral dimension of the Sierpinski gasket type of fractalsJournal of Physics A: General Physics, 1987
- Tethered surfaces: Statics and dynamicsPhysical Review A, 1987
- Critical exponents of the self-avoiding walks on a family of finitely ramified fractalsJournal of Physics A: General Physics, 1987
- Percolative conduction and the Alexander-Orbach conjecture in two dimensionsPhysical Review B, 1984
- Renormalisation on Sierpinski-type fractalsJournal of Physics A: General Physics, 1984