Issues

 / 

1991

 / 

September

  

Reviews of topical problems


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 $N\to\infty$.

Fulltext pdf (715 KB)
Fulltext is also available at DOI: 10.1070/PU1991v034n09ABEH002473
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)
BibTex BibNote ® (generic)BibNote ® (RIS)MedlineRefWorks
%0 Journal Article
%T The self-avoiding walk problem
%A V. I. Alkhimov
%I Physics-Uspekhi
%D 1991
%J Phys. Usp.
%V 34
%N 9
%P 804-816
%U https://ufn.ru/en/articles/1991/9/c/
%U https://doi.org/10.1070/PU1991v034n09ABEH002473

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

© 1918–2024 Uspekhi Fizicheskikh Nauk
Email: ufn@ufn.ru Editorial office contacts About the journal Terms and conditions