Self-avoiding walk with a topological obstacle

Puri, S. ; Schaub, B. ; Oono, Y. (1986) Self-avoiding walk with a topological obstacle Physical Review A, 34 (1). pp. 541-547. ISSN 1050-2947

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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.

Item Type:Article
Source:Copyright of this article belongs to The American Physical Society.
ID Code:32360
Deposited On:17 Mar 2011 09:42
Last Modified:10 Jun 2011 05:22

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