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
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
SN - 0022-4715
VL - 109
SP - 39
EP - 66
JO - Journal of Statistical Physics
JF - Journal of Statistical Physics
IS - 1-2
ER -