Minimization of the discrete interaction energy with smooth potentials
Mathematical Physics
2024-12-05 v1 math.MP
Abstract
We study the pair interaction on flat tori of functions whose Fourier coefficients are positive and decay sufficiently rapidly. In dimension one we find that the minimizer, up to translation, is the equidistant point set. In dimension two, minimizing with respect to triplets we find that the minimizer is the triangular lattice.
Cite
@article{arxiv.2412.03425,
title = {Minimization of the discrete interaction energy with smooth potentials},
author = {Yaniv Almog},
journal= {arXiv preprint arXiv:2412.03425},
year = {2024}
}