The Square Sticky Disk: Crystallization and Gamma-Convergence to the Octagonal Anisotropic Perimeter
Abstract
Abstract. We consider a variant of the sticky disk energy where distances between particles are evaluated through the sup norm [Formula: see text] in the plane. We first prove crystallization of minimizers in the square lattice, for any fixed number [Formula: see text] of particles. Then we consider the limit as [Formula: see text]: in contrast to the standard sticky disk, there is only one orientation in the limit, and we are able to compute explicitly the [Formula: see text]-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 [ 10 ] in the triangular case.
Fields of Study & Subjects
Stochastic processes and statistical mechanics
Nonlinear Partial Differential Equations
Mathematical Approximation and Integration
Publication details
- Journal / source
- SIAM Journal on Mathematical Analysis
- Volume
- 58
- Issue
- 3
- Pages
- 3238–3266
- Publication date
- 24 June 2026
- Language
- EN