Crystallization to the Square Lattice for a Two-Body Potential

@article{Btermin2019CrystallizationTT,
  title={Crystallization to the Square Lattice for a Two-Body Potential},
  author={Laurent B{\'e}termin and Lucia De Luca and Mircea Petrache},
  journal={arXiv: Analysis of PDEs},
  year={2019}
}
We consider two-dimensional zero-temperature systems of $N$ particles to which we associate an energy of the form $$ \mathcal{E}[V](X):=\sum_{1\le i<j\le N}V(|X(i)-X(j)|), $$ where $X(j)\in\mathbb R^2$ represents the position of the particle $j$ and $V(r)\in\mathbb R$ is the {pairwise interaction} energy potential of two particles placed at distance $r$. We show that under suitable assumptions on the single-well potential $V$, the ground state energy per particle converges to an explicit… 
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  • Laurent Bétermin
  • Computer Science
    Journal of Physics A: Mathematical and Theoretical
  • 2021
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