A crystallization result in two dimensions for a soft disc affine potential
Mathematical Physics
2023-05-12 v1 math.MP
Abstract
We prove finite crystallization for particles in the plane interacting through a soft disc potential, as originally shown by C. Radin \cite{Radin_soft}. We give an alternative proof that relies on the geometric decomposition of the energy proved in \cite{DLF1}, and that is based on showing that any minimizer has at least as many boundary points as the canonical ``spiral'' configuration.
Keywords
Cite
@article{arxiv.2305.06449,
title = {A crystallization result in two dimensions for a soft disc affine potential},
author = {Giacomo Del Nin and Lucia De Luca},
journal= {arXiv preprint arXiv:2305.06449},
year = {2023}
}