OpenAlex ·
BCC optimality for the three-dimensional Coulomb lattice energy
- Published
- Source
- OpenAlex
- Published in
- arXiv (Cornell University)
- DOI
- 10.48550/arxiv.2610.29732
- Original
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Abstract
We prove that the body-centered cubic lattice uniquely minimizes the renormalized Coulomb energy among three-dimensional Bravais lattices of fixed covolume, up to orthogonal transformations. Using Ewald summation, we write the energy, to within an additive constant, as a sum of two positive, rapidly convergent series in real and reciprocal space. Their positivity provides finite lower bounds for all competitors. A passage to the dual lattice reduces the problem to a face-centered cubic comparison. A short basis vector estimate, a certified local Hessian, and interval bounds on a compact five-dimensional domain complete the computer-assisted proof.
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