# The connective constant of the honeycomb lattice equals $\sqrt{2+\sqrt2}$

@article{DuminilCopin2010TheCC, title={The connective constant of the honeycomb lattice equals \$\sqrt\{2+\sqrt2\}\$}, author={Hugo Duminil-Copin and Stanislav Smirnov}, journal={arXiv: Mathematical Physics}, year={2010} }

We provide the first mathematical proof that the connective constant of the hexagonal lattice is equal to $\sqrt{2+\sqrt 2}$. This value has been derived non rigorously by B. Nienhuis in 1982, using Coulomb gas approach from theoretical physics. Our proof uses a parafermionic observable for the self avoiding walk, which satisfies a half of the discrete Cauchy-Riemann relations. Establishing the other half of the relations (which conjecturally holds in the scaling limit) would also imply…

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