Self-avoiding walks and polygons on the triangular lattice

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19 Citations (Scopus)

Abstract

We use new algorithms, based on the finite lattice method of series expansion, to extend the enumeration of self-avoiding walks and polygons on the triangular lattice to length 40 and 60, respectively. For self-avoiding walks to length 40 we also calculate series for the metric properties of mean-square end-to-end distance, mean-square radius of gyration and the mean-square distance of a monomer from the end points. For self-avoiding polygons to length 58 we calculate series for the mean-square radius of gyration and the first 10 moments of the area. Analysis of the series yields accurate estimates for the connective constant of triangular self-avoiding walks, = 4.150 797 226(26), and confirms to a high degree of accuracy several theoretical predictions for universal critical exponents and amplitude combinations.

Original languageEnglish
Article numberP10008
JournalJournal of Statistical Mechanics: Theory and Experiment
Issue number10
DOIs
Publication statusPublished - Oct 2004
Externally publishedYes

Keywords

  • critical exponents and amplitudes (theory)
  • series expansions

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