# 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, +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

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## PR ] 6 M ay 2 01 3 ON THE PROBABILITY THAT SELF-AVOIDING WALK ENDS AT A GIVEN

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