BCC optimality for the three-dimensional Coulomb lattice energy

C. B. Muratov; M. Novaga

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arXiv · 2610.29732

BCC optimality for the three-dimensional Coulomb lattice energy

C. B. Muratov·M. Novaga

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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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C. B. Muratov, M. Novaga. 2026-10-21. BCC optimality for the three-dimensional Coulomb lattice energy. https://arxiv.org/abs/2610.29732

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