The Critical Fugacity for Surface Adsorption of Self-Avoiding Walks on the Honeycomb Lattice is $${1+\sqrt{2}}$$1+2

@article{Beaton2014TheCF,
  title={The Critical Fugacity for Surface Adsorption of Self-Avoiding Walks on the Honeycomb Lattice is \$\$\{1+\sqrt\{2\}\}\$\$1+2},
  author={Nicholas R. Beaton and Mireille Bousquet-M{\'e}lou and Jan de Gier and Hugo Duminil-Copin and Anthony J. Guttmann},
  journal={Communications in Mathematical Physics},
  year={2014},
  volume={326},
  pages={727-754}
}
  • Nicholas R. Beaton, Mireille Bousquet-Mélou, +2 authors Anthony J. Guttmann
  • Published 2014
  • Physics, Mathematics
  • In 2010, Duminil-Copin and Smirnov proved a long-standing conjecture of Nienhuis, made in 1982, that the growth constant of self-avoiding walks on the hexagonal (a.k.a. honeycomb) lattice is $${\mu=\sqrt{2+\sqrt{2}}}$$μ=2+2. A key identity used in that proof was later generalised by Smirnov so as to apply to a general O(n) loop model with $${n\in [-2,2]}$$n∈[-2,2] (the case n = 0 corresponding to self-avoiding walks). We modify this model by restricting to a half-plane and introducing a surface… CONTINUE READING

    Create an AI-powered research feed to stay up to date with new papers like this posted to ArXiv

    References

    Publications referenced by this paper.