Sufficient Condition for a Compact Local Minimality of a Lattice

TL;DR

This paper establishes a sufficient condition under which a Bravais lattice in any dimension is locally minimal for its total energy, based on a family of radial long-range potentials, extending ideas from two-dimensional crystallization.

Contribution

It introduces a new sufficient condition for local minimality of Bravais lattices in any dimension, generalizing previous two-dimensional results.

Findings

Provides a criterion for local minimality based on potential parameters.

Extends crystallization results to higher dimensions.

Offers insights into energy minimization in lattice structures.

Abstract

We give a sufficient condition on a family of radial parametrized long-range potentials for a compact local minimality of a given $d$-dimensional Bravais lattice for its total energy of interaction created by each potential. This work is widely inspired by the paper of F. Theil about two dimensional crystallization.