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arXiv · 1907.06105

Crystallization to the square lattice for a two-body potential

Laurent Bétermin·Lucia De Luca·Mircea Petrache
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Abstract

We consider two-dimensional zero-temperature systems of $N$ particles to which we associate an energy of the form $$ \mathcal{E}[V](X):=\sum_{1\le i \sqrt{2}$, in which case ${\bar{\mathcal E}_{\mathrm{sq}}[V]}=-4$. To the best of our knowledge, this is the first proof of crystallization to the square lattice for a two-body interaction energy.

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Laurent Bétermin, Lucia De Luca, Mircea Petrache. 2019-10-23. Crystallization to the square lattice for a two-body potential. https://arxiv.org/abs/1907.06105

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