New approximate renormalization method on fractals

Kumiko Hattori; Tetsuya Hattori; Hiroshi Watanabe

doi:10.1103/PhysRevA.32.3730

New approximate renormalization method on fractals

Kumiko Hattori, Tetsuya Hattori, Hiroshi Watanabe

Research output: Contribution to journal › Article › peer-review

15 Citations (Scopus)

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.

Original language	English
Pages (from-to)	3730-3733
Number of pages	4
Journal	Physical Review A
Volume	32
Issue number	6
DOIs	https://doi.org/10.1103/PhysRevA.32.3730
Publication status	Published - 1985 Jan 1
Externally published	Yes

ASJC Scopus subject areas

Atomic and Molecular Physics, and Optics

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title = "New approximate renormalization method on fractals",

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 Sierpi{\'n}ski type, the results are smaller than the values obtained by the Migdal-Kadanoff renormalization.",

author = "Kumiko Hattori and Tetsuya Hattori and Hiroshi Watanabe",

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AU - Watanabe, Hiroshi

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AB - 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.

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