A new transfer-matrix algorithm for exact enumerations: self-avoiding walks on the square lattice
Mathematical Physics
2013-09-27 v1 Statistical Mechanics
math.MP
Abstract
We recently published [J. Phys A: Math. Theor. {\bf 45} 115202 (2012)] a new and more efficient implementation of a transfer-matrix algorithm for exact enumerations of self-avoiding polygons. Here we extend this work to the enumeration of self-avoiding walks on the square lattice. A detailed comparison with our previous best algorithm shows very significant improvement in the running time of the new algorithm. The new algorithm is used to extend the enumeration of self-avoiding walks to length 79 from the previous record of 71 and for metric properties, such as the average end-to-end distance, from 59 to 71.
Keywords
Cite
@article{arxiv.1309.6709,
title = {A new transfer-matrix algorithm for exact enumerations: self-avoiding walks on the square lattice},
author = {Iwan Jensen},
journal= {arXiv preprint arXiv:1309.6709},
year = {2013}
}
Comments
19 pages, 9 figures. arXiv admin note: substantial text overlap with arXiv:1111.5877