### 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 language | English (US) |
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Pages (from-to) | 541-547 |

Number of pages | 7 |

Journal | Physical Review A |

Volume | 34 |

Issue number | 1 |

DOIs | |

State | Published - Jan 1 1986 |

### ASJC Scopus subject areas

- Atomic and Molecular Physics, and Optics

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## Cite this

*Physical Review A*,

*34*(1), 541-547. https://doi.org/10.1103/PhysRevA.34.541