Self-avoiding polygons on the square lattice

Iwan Jensen; Anthony J. Guttmann

doi:10.1088/0305-4470/32/26/305

Self-avoiding polygons on the square lattice

Iwan Jensen, Anthony J. Guttmann

Research output: Contribution to journal › Article › peer-review

69 Citations (Scopus)

Abstract

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 = 2.638 158 529 27(1) (biased) and the critical exponent α = 0.500 0005(10) (unbiased). The critical point is indistinguishable from a root of the polynomial 581x⁴ + 7x² - 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.

Original language	English
Pages (from-to)	4867-4876
Number of pages	10
Journal	Journal of Physics A: Mathematical and General
Volume	32
Issue number	26
DOIs	https://doi.org/10.1088/0305-4470/32/26/305
Publication status	Published - 2 Jul 1999
Externally published	Yes

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AB - 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 = 2.638 158 529 27(1) (biased) and the critical exponent α = 0.500 0005(10) (unbiased). The critical point is indistinguishable from a root of the polynomial 581x4 + 7x2 - 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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