A new transfer-matrix algorithm for exact enumerations: self-avoiding polygons on the square lattice

Nathan Clisby; Iwan Jensen

doi:10.1088/1751-8113/45/11/115202

A new transfer-matrix algorithm for exact enumerations: self-avoiding polygons on the square lattice

Nathan Clisby
, Iwan Jensen

Research output: Contribution to journal › Article › peer-review

33 Citations (Scopus)

Abstract

We present a new and more efficient implementation of transfer-matrix methods for exact enumerations of lattice objects. The new method is illustrated by an application to the enumeration of self-avoiding polygons on the square lattice. A detailed comparison with the previous best algorithm shows significant improvement in the running time of the algorithm. The new algorithm is used to extend the enumeration of polygons to length 130 from the previous record of 110.

Original language	English
Article number	115202
Number of pages	15
Journal	Journal of Physics. A: Mathematical and Theoretical
Volume	45
Issue number	11
DOIs	https://doi.org/10.1088/1751-8113/45/11/115202
Publication status	Published - 28 Feb 2012
Externally published	Yes

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abstract = "We present a new and more efficient implementation of transfer-matrix methods for exact enumerations of lattice objects. The new method is illustrated by an application to the enumeration of self-avoiding polygons on the square lattice. A detailed comparison with the previous best algorithm shows significant improvement in the running time of the algorithm. The new algorithm is used to extend the enumeration of polygons to length 130 from the previous record of 110.",

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AB - We present a new and more efficient implementation of transfer-matrix methods for exact enumerations of lattice objects. The new method is illustrated by an application to the enumeration of self-avoiding polygons on the square lattice. A detailed comparison with the previous best algorithm shows significant improvement in the running time of the algorithm. The new algorithm is used to extend the enumeration of polygons to length 130 from the previous record of 110.

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UR - http://purl.org/au-research/grants/ARC/DP0770705

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M3 - Article

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A new transfer-matrix algorithm for exact enumerations: self-avoiding polygons on the square lattice

Abstract

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