Self-avoiding walks and polygons crossing a domain on the square and hexagonal lattices

  title={Self-avoiding walks and polygons crossing a domain on the square and hexagonal lattices},
  author={Anthony J. Guttmann and Iwan Jensen},
  journal={Journal of Physics A: Mathematical and Theoretical},
  • A. GuttmannI. Jensen
  • Published 13 August 2022
  • Mathematics
  • Journal of Physics A: Mathematical and Theoretical
We have analysed the recently extended series for the number of self-avoiding walks (SAWs) CL(1) that cross an L × L square between diagonally opposed corners. The number of such walks is known to grow as λSL2. We have made more precise the estimate of λS, based on additional series coefficients provided by several authors, and refined analysis techniques. We estimate that λS=1.7445498±0.0000012. We have also studied the subdominant behaviour, and conjecture that CL(1)∼λSL2+bL+c⋅Lg, where b=−0… 

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