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A parallel algorithm for the enumeration of self-avoiding polygons on the square lattice

Iwan Jensen
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Abstract

We have developed a parallel algorithm that allows us to enumerate the number of self-avoiding polygons on the square lattice to perimeter length 110. We have also extended the series for the first 10 area-weighted moments and the radius of gyration to 100. Analysis of the resulting series yields very accurate estimates of the connective constant $μ=2.63815853031(3)$ (biased) and the critical exponent $α= 0.5000001(2)$ (unbiased). In addition we obtain very accurate estimates for the leading amplitudes confirming to a high degree of accuracy various predictions for universal amplitude combinations.

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Iwan Jensen. 2003-01-24. A parallel algorithm for the enumeration of self-avoiding polygons on the square lattice. https://doi.org/10.1088/0305-4470%2F36%2F21%2F304

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