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arXiv · 2503.22895

Critical modular lattices in the Gaussian core model

Arian Joharian·Frank Vallentin·Marc Christian Zimmermannn
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Abstract

We discuss the local analysis of Gaussian potential energy of modular lattices. We present examples of $2$-modular lattices -- such as the $16$-dimensional Barnes-Wall lattice -- and $3$-modular lattices -- such as the $12$-dimensional Coxeter-Todd lattice -- that are locally universally optimal among lattices (in the sense of Cohn and Kumar). We also provide other $2$- and $3$-modular lattices that are not locally universally optimal, or not even critical in the Gaussian core model.

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Arian Joharian, Frank Vallentin, Marc Christian Zimmermannn. 2025-03-28. Critical modular lattices in the Gaussian core model. https://arxiv.org/abs/2503.22895

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