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

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 $\mu =2.63815853031(3)$ (biased) and the critical exponent $\alpha =0.5000001(2)$ (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.

arXiv comment17 pages, 5 figures

References in corpus (6)

• Self-avoiding polygons on the square lattice
• Algebraic Techniques for Enumerating Self-Avoiding Walks on the Square Lattice
• Universal Amplitude Combinations for Self-Avoiding Walks, Polygons and Trails
• Mean Area of Self-Avoiding Loops
• Scaling function and universal amplitude combinations for self-avoiding polygons
• Size and area of square lattice polygons

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