2010/07/04 by Hugo Duminil‐Copin, Stanislav Smirnov, Duminil-Copin, Hugo +1
Physics and Astronomy · Mathematics · #Theoretical and Computational Physics #Stochastic processes and statistical mechanics #Random Matrices and Applications
paper · pdf · doi:10.48550/arxiv.1007.0575
We provide the first mathematical proof that the connective constant of the\nhexagonal lattice is equal to \√(2+\√ 2). This value has been derived\nnon rigorously by B. Nienhuis in 1982, using Coulomb gas approach from\ntheoretical physics. Our proof uses a parafermionic observable for the self\navoiding walk, which satisfies a half of the discrete Cauchy-Riemann relations.\nEstablishing the other half of the relations (which conjecturally holds in the\nscaling limit) would also imply convergence of the self-avoiding walk to\nSLE(8/3).\n