Asymptotic behavior of the "true" self-avoiding walk

Daniel J. Amit, G. Parisi, and L. Peliti
Phys. Rev. B 27, 1635 – Published 1 February 1983
PDFExport Citation

Abstract

The "true" self-avoiding random walk is defined as the statistical problem of a traveler who steps randomly, but tries to avoid places he has already visited. We show that this problem is different from the problem of a self-repelling chain (polymer problem). Most striking is perhaps the fact that the upper critical dimensionality of such a walk is 2. Renormalization-group theory is applied to compute logarithmic corrections to ordinary random-walk behavior in two dimensions. The theoretical predictions are confirmed by computer simulations.

  • Received 27 September 1982

DOI:https://doi.org/10.1103/PhysRevB.27.1635

©1983 American Physical Society

Authors & Affiliations

Daniel J. Amit*

  • Racah Institute of Physics, Hebrew University, Jerusalem, Israel

G. Parisi

  • Universita di Roma II, Tor Vergata, Roma, Italy and Istituto Nazionale di Física Nucleare, Laboratori Nationali di Frascati, Frascati, Italy

L. Peliti

  • Istituto di Fisica "G. Marconi," Roma, Italy and Gruppo Nazionale de Struttura della Materia-Consiglio Nazionale delle Ricerche, Unita di Roma, Roma, Italy

  • *Address until June 1983: Institute for Advanced Study, Princeton, NJ 08540.

References (Subscription Required)

Click to Expand
Issue

Vol. 27, Iss. 3 — 1 February 1983

Reuse & Permissions
Access Options
Author publication services for translation and copyediting assistance advertisement

Authorization Required


×
×

Images

×

Sign up to receive regular email alerts from Physical Review B

Log In

Cancel
×

Search


Article Lookup

Paste a citation or DOI

Enter a citation
×