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arXiv · 2105.07868

Critical even unimodular lattices in the Gaussian core model

Arne Heimendahl·Aurelio Marafioti·Antonia Thiemeyer·Frank Vallentin·Marc Christian Zimmermann
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Abstract

We consider even unimodular lattices which are critical for potential energy with respect to Gaussian potential functions in the manifold of lattices having point density 1. All even unimodular lattices up to dimension 24 are critical. We show how to determine the Morse index in these cases. While all these lattices are either local minima or saddle points, we find lattices in dimension 32 which are local maxima. Also starting from dimension 32 there are non-critical even unimodular lattices.

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Arne Heimendahl, Aurelio Marafioti, Antonia Thiemeyer, Frank Vallentin, Marc Christian Zimmermann. 2021-05-17. Critical even unimodular lattices in the Gaussian core model. https://doi.org/10.1093/imrn%2Frnac164

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