The hexagonal lattice is universally locally optimal
Metric Geometry
2025-11-06 v1 Mathematical Physics
math.MP
Abstract
We prove that the hexagonal lattice is a local minimizer, among all point configurations, of the interaction energy per unit volume for pair potentials that are completely monotonic functions of the square distance. This includes Gaussian interactions and power laws.
Keywords
Cite
@article{arxiv.2511.03353,
title = {The hexagonal lattice is universally locally optimal},
author = {Thomas Leblé},
journal= {arXiv preprint arXiv:2511.03353},
year = {2025}
}
Comments
39 pages, comments welcome