▎ 摘 要
Graphene samples are identified as minimizers of configurational energies featuring both two- and three-body atomic-interaction terms. This variational viewpoint allows for a detailed description of ground-state geometries as connected subsets of a regular hexagonal lattice. We investigate here how these geometries evolve as the number n of carbon atoms in the graphene sample increases. By means of an equivalent characterization of minimality via a discrete isoperimetric inequality, we prove that ground states converge to the ideal hexagonal Wulff shape as n -> infinity. Precisely, ground states deviate from such hexagonal Wulff shape by at most Kn(3/4) + o(n(3/4)) atoms, where both the constant K and the rate n(3/4) are sharp.