Self-avoiding walk with a topological obstacle
- 1 July 1986
- journal article
- research article
- Published by American Physical Society (APS) in Physical Review A
- Vol. 34 (1), 541-547
- https://doi.org/10.1103/physreva.34.541
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 ε-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.Keywords
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