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Self-avoiding polygons on the square lattice

Iwan Jensen·Anthony J Guttmann
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Abstract

We have developed an improved algorithm that allows us to enumerate the number of self-avoiding polygons on the square lattice to perimeter length 90. Analysis of the resulting series yields very accurate estimates of the connective constant $μ=2.63815852927(1)$ (biased) and the critical exponent $α= 0.5000005(10)$ (unbiased). The critical point is indistinguishable from a root of the polynomial $581x^4 + 7x^2 - 13 =0.$ An asymptotic expansion for the coefficients is given for all $n.$ There is strong evidence for the absence of any non-analytic correction-to-scaling exponent.

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Iwan Jensen, Anthony J Guttmann. 1999-05-19. Self-avoiding polygons on the square lattice. https://doi.org/10.1088/0305-4470%2F32%2F26%2F305

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