Year: 2026
Type: preprint
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.
Source: arXiv (Cornell University)
Authors: Muratov, C. B., Novaga, M.
Institution: University of Pisa
Language: English
Subfield: Numerical Analysis
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7223236171