A crystallization result in two dimensions for a soft disc affine potential

2023/05/10 by Giacomo Del Nin, Del Nin, Giacomo, Lucia De Luca +1 · 1 citation
Engineering · Mathematics · #Composite Material Mechanics #FOS: Physical sciences #Mathematical Approximation and Integration #Mathematical Physics (math-ph) #Spectral Theory in Mathematical Physics

paper · pdf · doi:10.48550/arxiv.2305.06449

openalex publication_date 2023/05/10 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We prove finite crystallization for particles in the plane interacting through a soft disc potential, as originally shown by C. Radin \citeRadin_soft. We give an alternative proof that relies on the geometric decomposition of the energy proved in \citeDLF1, and that is based on showing that any minimizer has at least as many boundary points as the canonical ``spiral'' configuration.

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