Minimization of energy per particle among Bravais lattices in ℝ 2 : Lennard–Jones and Thomas–Fermi cases

Source abstract

We prove in this paper that the minimizer of Lennard–Jones energy per particle among Bravais lattices is a triangular lattice, i.e. composed of equilateral triangles, in ℝ 2 for large density of points, while it is false for sufficiently small density. We show some characterization results for the global minimizer of this energy and finally we also prove that the minimizer of the Thomas–Fermi energy per particle in ℝ 2 among Bravais lattices with fixed density is triangular.