Self-avoiding walk enumeration via the lace expansion
N. Clisby, R. Liang, and G. Slade. Abstract Book of the XXIII IUPAP International Conference on Statistical Physics, Genova, Italy, (9-13 July 2007)
Abstract
We introduce a new method for the enumeration of self-avoiding
walks based on the lace expansion. We also introduce an
algorithmic improvement, called the two-step method, for
self-avoiding walk enumeration problems. We obtain significant
extensions of existing series on the cubic and hypercubic lattices
in all dimensions $d 3$: we enumerate $32$-step self-avoiding
polygons in $d=3$, $26$-step self-avoiding polygons in $d=4$,
$30$-step self-avoiding walks in $d=3$, and $24$-step
self-avoiding walks and polygons in all dimensions $d \geq
4$.
%0 Book Section
%1 statphys23_0949
%A Clisby, N.
%A Liang, R.
%A Slade, G.
%B Abstract Book of the XXIII IUPAP International Conference on Statistical Physics
%C Genova, Italy
%D 2007
%E Pietronero, Luciano
%E Loreto, Vittorio
%E Zapperi, Stefano
%K critical enumeration lattice phenomena self-avoiding statphys23 topic-2 walk
%T Self-avoiding walk enumeration via the lace expansion
%U http://st23.statphys23.org/webservices/abstract/preview_pop.php?ID_PAPER=949
%X We introduce a new method for the enumeration of self-avoiding
walks based on the lace expansion. We also introduce an
algorithmic improvement, called the two-step method, for
self-avoiding walk enumeration problems. We obtain significant
extensions of existing series on the cubic and hypercubic lattices
in all dimensions $d 3$: we enumerate $32$-step self-avoiding
polygons in $d=3$, $26$-step self-avoiding polygons in $d=4$,
$30$-step self-avoiding walks in $d=3$, and $24$-step
self-avoiding walks and polygons in all dimensions $d \geq
4$.
@incollection{statphys23_0949,
abstract = {We introduce a new method for the enumeration of self-avoiding
walks based on the lace expansion. We also introduce an
algorithmic improvement, called the two-step method, for
self-avoiding walk enumeration problems. We obtain significant
extensions of existing series on the cubic and hypercubic lattices
in all dimensions $d \geq 3$: we enumerate $32$-step self-avoiding
polygons in $d=3$, $26$-step self-avoiding polygons in $d=4$,
$30$-step self-avoiding walks in $d=3$, and $24$-step
self-avoiding walks and polygons in \emph{all} dimensions $d \geq
4$.},
added-at = {2007-06-20T10:16:09.000+0200},
address = {Genova, Italy},
author = {Clisby, N. and Liang, R. and Slade, G.},
biburl = {https://www.bibsonomy.org/bibtex/2c5497156e7a961779e891609d5a97ed3/statphys23},
booktitle = {Abstract Book of the XXIII IUPAP International Conference on Statistical Physics},
editor = {Pietronero, Luciano and Loreto, Vittorio and Zapperi, Stefano},
interhash = {5be1c4d71bdf1308f97727e10be48d8d},
intrahash = {c5497156e7a961779e891609d5a97ed3},
keywords = {critical enumeration lattice phenomena self-avoiding statphys23 topic-2 walk},
month = {9-13 July},
timestamp = {2007-06-20T10:16:35.000+0200},
title = {Self-avoiding walk enumeration via the lace expansion},
url = {http://st23.statphys23.org/webservices/abstract/preview_pop.php?ID_PAPER=949},
year = 2007
}