Critical modular lattices in the Gaussian core model
Metric Geometry
2026-02-20 v2 Number Theory
Abstract
We discuss the local analysis of Gaussian potential energy of modular lattices. We present examples of -modular lattices -- such as the -dimensional Barnes-Wall lattice -- and -modular lattices -- such as the -dimensional Coxeter-Todd lattice -- that are locally universally optimal among lattices (in the sense of Cohn and Kumar). We also provide other - and -modular lattices that are not locally universally optimal, or not even critical in the Gaussian core model.
Cite
@article{arxiv.2503.22895,
title = {Critical modular lattices in the Gaussian core model},
author = {Arian Joharian and Frank Vallentin and Marc Christian Zimmermannn},
journal= {arXiv preprint arXiv:2503.22895},
year = {2026}
}
Comments
32 pages, (v2): Computational results reported in Section 5 were wrong in (v1), due to an indexing mistake. Now corrected and thoroughly checked, relevant parts completely rewritten