The self-avoiding walk problem

Different approaches to the self-avoiding walk problem are reviewed. The problem first arose in the statistical physics of linear polymers in connection with the evaluation of the average size of a polymer. The probability distribution density $W_N(\mathbf{R})$ for the vector $\mathbf{R}$ connecting the end-points of an $N$-step self-avoiding walk is the main quantity in this problem. The equation for $W_N(\mathbf{R})$ seems to be invariant under the scaling transformation group. This means that the renormalization group method can be used to determine the asymptotic form of $W_N(\mathbf{R})$ as $N\to\infty$.

PACS: 05.40.Fb, 64.60.Ak, 64.60.Fr (all)
DOI: 10.1070/PU1991v034n09ABEH002473
URL: https://ufn.ru/en/articles/1991/9/c/
Citation: Alkhimov V I "The self-avoiding walk problem" Sov. Phys. Usp. 34 (9) 804–816 (1991)

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Оригинал: Алхимов В И «Проблема случайных блужданий без самопересечений» УФН 161 (9) 133–160 (1991); DOI: 10.3367/UFNr.0161.199109c.0133

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