%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 }