Iwan Jensen and Anthony J Guttmann 1999 J. Phys. A: Math. Gen. 32 4867 doi:10.1088/0305-4470/32/26/305
Self-avoiding polygons on the square lattice
Iwan Jensen and Anthony J Guttmann
Show affiliationsWe 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 
=2.638 158 529 27(1) (biased) and the critical exponent 
= 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.
- PACS
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05.50.+q Lattice theory and statistics (Ising, Potts, etc.)
- MSC
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82B20 Lattice systems (Ising, dimer, Potts, etc.) and systems on graphs
82B41 Random walks, random surfaces, lattice animals, etc. (See also 60G50, 82C41)
33C52 Orthogonal polynomials and functions associated with root systems
- Subjects
- Dates
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Issue 26 (2 July 1999)
Received 25 February 1999, in final form 30 April 1999
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Self-avoiding polygons on the square lattice
Iwan Jensen and Anthony J Guttmann 1999 J. Phys. A: Math. Gen. 32 4867
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