Enumeration of self-avoiding walks on the square lattice

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Abstract

We describe a new algorithm for the enumeration of self-avoiding walks on the square lattice. Using up to 128 processors on a HP Alpha server cluster we have enumerated the number of self-avoiding walks on the square lattice to length 71. Series for the metric properties of mean-square end-to-end distance, mean-square radius of gyration and mean-square distance of monomers from the end points have been derived to length 59. An analysis of the resulting series yields accurate estimates of the critical exponents γ and ν confirming predictions of their exact values. Likewise we obtain accurate amplitude estimates yielding precise values for certain universal amplitude combinations. Finally we report on an analysis giving compelling evidence that the leading non-analytic correction-to-scaling exponent Δ1 = 3/2.

Original languageEnglish
Pages (from-to)5503-5524
Number of pages22
JournalJournal of Physics A: Mathematical and General
Volume37
Issue number21
DOIs
Publication statusPublished - 28 May 2004
Externally publishedYes

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