$$\varGamma $$Γ-Convergence of the Heitmann–Radin Sticky Disc Energy to the Crystalline Perimeter

  title={\$\$\varGamma \$\$$\Gamma$-Convergence of the Heitmann–Radin Sticky Disc Energy to the Crystalline Perimeter},
  author={Lucia De Luca and Matteo Novaga and Marcello Ponsiglione},
  journal={Journal of Nonlinear Science},
We consider low-energy configurations for the Heitmann–Radin sticky discs functional, in the limit of diverging number of discs. More precisely, we renormalize the Heitmann–Radin potential by subtracting the minimal energy per particle, i.e. the so-called kissing number. For configurations whose energy scales like the perimeter, we prove a compactness result which shows the emergence of polycrystalline structures: The empirical measure converges to a set of finite perimeter, while a microscopic… 
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