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

Submitted to Annals of Mathematics. 2012, vol. 175, no. 3, p. 1653-1665
Abstract 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 convergence of the self-avoiding walk to SLE(8/3).
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DUMINIL-COPIN, Hugo, SMIRNOV, Stanislav. The connective constant of the honeycomb lattice equals $sqrt{2+sqrt2}$. Submitted to: Annals of Mathematics, 2012, vol. 175, n° 3, p. 1653-1665. https://archive-ouverte.unige.ch/unige:11959

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Deposited on : 2010-09-30

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