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

2013/09/26 by Iwan Jensen, Jensen, Iwan · 1 citation
Computer Science · Mathematics · #Advanced Combinatorial Mathematics #Algorithms and Data Compression #Cellular Automata and Applications #FOS: Physical sciences #Mathematical Physics (math-ph) #Statistical Mechanics (cond-mat.stat-mech)

paper · pdf · doi:10.48550/arxiv.1309.6709

openalex publication_date 2013/09/26 · openalex created_date 2022/09/09 · openalex updated_date 2026/07/28

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.

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