13.12.2018 17:30 Leonard Kreutz (Universität Wien):
Finite crystallization for ionic dimersRoom 2004, 1st floor, Building L1 (Universitätsstr. 14, 86159 Augsburg)

In this talk we will present some crystallization results of ionic dimers. In particular we consider finite discrete systems consisting of two different atomic types and investigate ground-state congurations for congurational energies featuring two- body short-ranged particle interactions. The atomic potentials favor some reference distance between different atomic types and include repulsive terms for atoms of the same type, which are typical assumptions in models for ionic dimers. Our goal is to show a two-dimensional crystallization result. More precisely, we give conditions in order to prove that energy minimizers are connected subsets of the hexagonal lattice where the two atomic types are alternately arranged in the crystal lattice. We also provide explicit formulas for the ground-state energy. Finally, we characterize the net charge, that means, the difference of the number of the two atomic types. Analyzing the deviation of congurations from the hexagonal Wulff shape, we prove that for ground states consisting of n particles the net charge is at most of order O(n^1/4) where the scaling is sharp.