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 | |
| Publication status | Published - 2 Jul 1999 |
| Externally published | Yes |
Fingerprint Dive into the research topics of 'Self-avoiding polygons on the square lattice'. Together they form a unique fingerprint.
Cite this
Jensen, I., & Guttmann, A. J. (1999). Self-avoiding polygons on the square lattice. Journal of Physics A: Mathematical and General, 32(26), 4867-4876. https://doi.org/10.1088/0305-4470/32/26/305