TY - JOUR

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

AU - Hattori, Tetsuya

AU - Tsuda, Toshiro

N1 - Funding Information:
T. Hattori thanks Prof. S. Kusuoka and Prof. K. Hattori for collaborations, and Prof. T. Hara for encouragements. The authors thank the members in Department of Mathematics, Rikkyo Univeristy, where part of this work was done, and the referee for detailed check of the proofs. The research of T. Hattori is supported in part by a Grant-in-Aid for Scientific Research (C) from the Ministry of Education, Culture, Sports, Science and Technology.

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

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U2 - 10.1023/A:1019927309542

DO - 10.1023/A:1019927309542

M3 - Article

AN - SCOPUS:0141627427

SN - 0022-4715

VL - 109

SP - 39

EP - 66

JO - Journal of Statistical Physics

JF - Journal of Statistical Physics

IS - 1-2

ER -