PreprintCC BY 4.0arXiv
BCC optimality for the three-dimensional Coulomb lattice energy
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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BibTeX
@misc{muratov2026optimality,
title = {{BCC optimality for the three-dimensional Coulomb lattice energy}},
author = {C. B. Muratov and M. Novaga},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.29732},
eprint = {2610.29732},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.29732},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - BCC optimality for the three-dimensional Coulomb lattice energy
AU - C. B. Muratov
AU - M. Novaga
PY - 2026
DA - 2026/10/21
PB - arXiv
DO - 10.48550/arxiv.2610.29732
UR - https://arxiv.org/abs/2610.29732
AB - 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.
ER -