The asymptotic behaviour of directed self-avoiding walks
- 21 August 1983
- journal article
- editorial
- Published by IOP Publishing in Journal of Physics A: General Physics
- Vol. 16 (12) , 2883-2885
- https://doi.org/10.1088/0305-4470/16/12/035
Abstract
Chakrabarti and Manna (1983) have made a numerical study of 'directed' self-avoiding walks on a square lattice, in which the random walker is forbidden to move upward: extrapolating from an enumeration of N-step walks up to N=14, they claimed that the mean end-to-end displacement, RN, behaves asymptotically for large N as Nnu with nu =0.86+or-0.02. It is shown that a simple application of the generating function method yields the behaviour of N-step walks of this type exactly (for all N), and the result nu =1 is rigorously proved.Keywords
This publication has 4 references indexed in Scilit:
- Critical behaviour of directed self-avoiding walksJournal of Physics A: General Physics, 1983
- Exact Critical Point and Critical Exponents ofModels in Two DimensionsPhysical Review Letters, 1982
- Excluded-Volume Problem and the Ising Model of FerromagnetismPhysical Review B, 1959
- Combinatorial Problems Suggested by the Statistical Mechanics of Domains and of Rubber-Like MoleculesPhysical Review B, 1956