Self-avoiding walk with a topological obstacle

S. Puri, B. Schaub, Y. Oono

Research output: Contribution to journalArticle

Abstract

The self-avoiding walk in the three-dimensional space with a topological obstacle an infinite rod is studied with the aid of a renormalization-group approach. Specifically, the mean winding number of the self-avoiding chain around the rod with both its ends fixed in space is calculated. The main interest of the problem is, however, a methodological one. Since the winding number is well defined only for no more than three dimensions, the -expansion method, so successful in the study of the self-avoiding chain, cannot be utilized. Instead, a variation of the method, the homotopy parameter expansion, is applied to the problem. This gives a nontrivial illustration of the method. The result suggests that the overall shape of the self-avoiding chain is less spherical than that for the simple random walk. This seems to be in conformity with the existing Monte Carlo result.

Original languageEnglish (US)
Pages (from-to)541-547
Number of pages7
JournalPhysical Review A
Volume34
Issue number1
DOIs
StatePublished - Jan 1 1986

ASJC Scopus subject areas

  • Atomic and Molecular Physics, and Optics

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