### 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 language | English |
---|---|

Pages (from-to) | 39-66 |

Number of pages | 28 |

Journal | Journal of Statistical Physics |

Volume | 109 |

Issue number | 1-2 |

DOIs | |

Publication status | Published - 2002 |

Externally published | Yes |

### Fingerprint

### 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.

Research output: Contribution to journal › Article

*Journal of Statistical Physics*, vol. 109, no. 1-2, pp. 39-66. https://doi.org/10.1023/A:1019927309542

}

TY - JOUR

T1 - Renormalization group analysis of the self-avoiding paths on the d-dimensional Sierpiński gaskets

AU - Hattori, Tetsuya

AU - Tsuda, Toshiro

PY - 2002

Y1 - 2002

N2 - 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.

AB - 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.

KW - Fractals

KW - Renormalization group

KW - Self-avoiding walk

KW - Sierpiński gasket

UR - http://www.scopus.com/inward/record.url?scp=0141627427&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0141627427&partnerID=8YFLogxK

U2 - 10.1023/A:1019927309542

DO - 10.1023/A:1019927309542

M3 - Article

AN - SCOPUS:0141627427

VL - 109

SP - 39

EP - 66

JO - Journal of Statistical Physics

JF - Journal of Statistical Physics

SN - 0022-4715

IS - 1-2

ER -