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
SN - 2469-9926
VL - 34
SP - 541
EP - 547
JO - Physical Review A
JF - Physical Review A
IS - 1
ER -