Quick search Find article
Quick search
Find article

Self-avoiding walks in two to five dimensions: exact enumerations and series study

D MacDonald, D L Hunter, K Kelly and N Jan

Show affiliations


The method of concatenation (the addition of precomputed shorter chains to the ends of a centrally generated longer chain) has permitted the extension of the exact series for CN-the number of distinct configurations for self-avoiding walks of length N. The authors report on the leading exponent y and xc (the reciprocal of the connectivity constant) for the 2D honeycomb lattice (42 terms) 1.3437, 0.541 1968; the 2D square lattice (30 terms) 1.3436, 0.379 0520; the 3D simple cubic lattice (23 terms) 1.161 932, 0.213 4987; the 4D hypercubic (18 terms) y approximately=1, 0.147 60 and the 5D hypercubic lattice (13 terms) y<or=1.025, 0.113 05. In addition they have also evaluated the leading correction terms: honeycomb Delta approximately=1, square Delta approximately=0.85, simple cubic Delta approximately=1.0 and the 4D hypercubic logarithmic correction with delta approximately=0.25.


PACS

05.40.Fb Random walks and Levy flights

05.50.+q Lattice theory and statistics (Ising, Potts, etc.)

MSC

82B41 Random walks, random surfaces, lattice animals, etc. (See also 60G50, 82C41)

82B20 Lattice systems (Ising, dimer, Potts, etc.) and systems on graphs

Subjects

Statistical physics and nonlinear systems

Dates

Issue 6 (21 March 1992)



View by subject




Export








Please login to access our web services, or create an account if you don't yet have one.

You must have cookies enabled in your web browser to be able to login.

Username
Password

Forgotten your password? Get a new one here.