New approximate renormalization method on fractals
- 1 December 1985
- journal article
- research article
- Published by American Physical Society (APS) in Physical Review A
- Vol. 32 (6) , 3730-3733
- https://doi.org/10.1103/physreva.32.3730
Abstract
We introduce a new approximate block-spin transformation, and applying this method to the massless free field on fractals, we obtain approximate values of the spectral dimension. For fractals of the Sierpiński type, the results are smaller than the values obtained by the Migdal-Kadanoff renormalization.Keywords
This publication has 14 references indexed in Scilit:
- The renormalization group and the ϵ expansionPublished by Elsevier ,2002
- Spectral dimension of a wire networkJournal of Physics A: General Physics, 1985
- Renormalisation on symmetric fractalsJournal of Physics A: General Physics, 1984
- Renormalisation on Sierpinski-type fractalsJournal of Physics A: General Physics, 1984
- A rigorous approach to Anderson localizationPhysics Reports, 1984
- Harmonic analysis in fractal spaces: Random walk statistics and spectrum of the Schrödinger equationPhysics Reports, 1984
- Solutions to the Schrödinger equation on some fractal latticesPhysical Review B, 1983
- Geometric Implementation of Hypercubic Lattices with Noninteger Dimensionality by Use of Low Lacunarity Fractal LatticesPhysical Review Letters, 1983
- Phase Transition and FractalsProgress of Theoretical Physics, 1983
- Random walks on fractal structures and percolation clustersJournal de Physique Lettres, 1983