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

Abstract We provide the first mathematical proof that the connective constant of the hexagonal lattice is equal to 2+2‾√‾‾‾‾‾‾‾√. This value has been derived nonrigorously 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 convergence of the self-avoiding walk to SLE(8/3).

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### 数学年刊（Annals of Mathematics）

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