TY - JOUR

T1 - Self-avoiding walk with a topological obstacle

AU - Puri, S.

AU - Schaub, B.

AU - Oono, Y.

PY - 1986

Y1 - 1986

N2 - 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.

AB - 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.

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U2 - 10.1103/PhysRevA.34.541

DO - 10.1103/PhysRevA.34.541

M3 - Article

AN - SCOPUS:35949020113

VL - 34

SP - 541

EP - 547

JO - Physical Review A

JF - Physical Review A

SN - 2469-9926

IS - 1

ER -