Minimization of the discrete interaction energy with smooth potentials

2024/12/04 by Almog, Yaniv
#42A16 #52C35 #52C99 #FOS: Physical sciences #Mathematical Physics (math-ph)

paper · doi:10.48550/arxiv.2412.03425

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.

Related

• A family of interaction energy minimizers supported on two intervals
• Optimal and non-optimal lattices for non-completely monotone interaction potentials
• Discrete minimizers of the interaction energy in collective behavior: a brief numerical and analytic review
• A family of explicit minimizers for interaction energies
• Riesz Energy on the Torus: Regularity of Minimizers