Renormalization group analysis of the self-avoiding paths on the d-dimensional Sierpiński gaskets

Tetsuya Hattori, Toshiro Tsuda

Research output: Contribution to journalArticle

7 Citations (Scopus)

Abstract

Notion of the renormalization group dynamical system, the self-avoiding fixed point and the critical trajectory are mathematically defined for the set of self-avoiding walks on the d-dimensional pre-Sierpiński gaskets (n-simplex lattices), such that their existence imply the asymptotic behaviors of the self-avoiding walks, such as the existence of the limit distributions of the scaled path lengths of "canonical ensemble," the connectivity constant (exponential growth of path numbers with respect to the length), and the exponent for mean square displacement. We apply the so defined framework to prove these asymptotic behaviors of the restricted self-avoiding walks on the 4-dimensional pre-Sierpiński gasket.

Original languageEnglish
Pages (from-to)39-66
Number of pages28
JournalJournal of Statistical Physics
Volume109
Issue number1-2
DOIs
Publication statusPublished - 2002
Externally publishedYes

Fingerprint

gaskets
Self-avoiding Walk
Renormalization Group
Path
Asymptotic Behavior
dynamical systems
Canonical Ensemble
trajectories
Limit Distribution
exponents
Path Length
Exponential Growth
Mean Square
Connectivity
Dynamical system
Fixed point
Exponent
Trajectory
Imply

Keywords

  • Fractals
  • Renormalization group
  • Self-avoiding walk
  • Sierpiński gasket

ASJC Scopus subject areas

  • Physics and Astronomy(all)
  • Statistical and Nonlinear Physics
  • Mathematical Physics

Cite this

Renormalization group analysis of the self-avoiding paths on the d-dimensional Sierpiński gaskets. / Hattori, Tetsuya; Tsuda, Toshiro.

In: Journal of Statistical Physics, Vol. 109, No. 1-2, 2002, p. 39-66.

Research output: Contribution to journalArticle

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