Wulff shape emergence in graphene
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 Precisely, ground states deviate from such hexagonal Wulff shape by at most Kn3/4 o(n3/4) atoms, where both the constant K and the rate n3/4 are sharp.