Preprint

Inserted: 22 mar 2025
Last Updated: 22 mar 2025

Year: 2025

Abstract:

We consider a variant of the sticky disk energy where distances between particles are evaluated through the sup norm $|\cdot|_{\infty}$ in the plane. We first prove crystallization of minimizers in the square lattice, for any  fixed number $N$ of particles. Then we consider the limit as $N \to\infty$: in contrast to the standard sticky disk, there is only one orientation in the limit, and we are able to compute explicitly the $\Gamma$-limit to be an anisotropic perimeter with octagonal Wulff  shape. The results are based on an energy decomposition for graphs that generalizes the one proved by De Luca-Friesecke in the triangular case.

Download:

• main.pdf