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 |
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Pages (from-to) | 4867-4876 |
Number of pages | 10 |
Journal | Journal of Physics A: Mathematical and General |
Volume | 32 |
Issue number | 26 |
DOIs | |
Publication status | Published - 2 Jul 1999 |
Externally published | Yes |