The hexagonal lattice is universally locally optimal

TL;DR

This paper proves that the hexagonal lattice configuration minimizes interaction energy locally among all point arrangements for a broad class of pair potentials, including Gaussian and power law interactions.

Contribution

It establishes the hexagonal lattice as a universal local energy minimizer for completely monotonic pair potentials.

Findings

Hexagonal lattice is a local energy minimizer.

Applicable to Gaussian and power law potentials.

Results hold among all point configurations.

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.