From interatomic potentials to Wulff shapes, via Gamma convergence

We investigate ground state configurations of atomic pair potential systems in two dimensions as the number of particles tends to infinity. Assuming crystallization (which has been proved for some cases such as the Radin potential, and is believed to hold more generally), we show that after suitable rescaling, the ground states converge to a unique macroscopic Wulff shape. Moreover, we derive a scaling law for the size of microscopic non-uniqueness which indicates larger fluctuations about the Wulff shape than intuitively expected.

Joint work with Yuen Au-Yeung and Bernd Schmidt (TU Munich),

to appear in Calc. Var. PDE