English

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}
}
R2 v1 2026-06-28T10:31:31.453Z