Repulsion in low temperature $β$-ensembles

Yacin Ameur

Published 2017-01-17Version 1

We prove a result on non-clustering of particles in a two-dimensional Coulomb plasma, which holds provided that the inverse temperature $\beta$ satisfies $\beta>1$. As a consequence we obtain a result on crystallization as $\beta\to\infty$: the particles will, on a microscopic scale, appear at a certain distance from each other. The estimation of this distance is connected to Abrikosov's conjecture that the particles should freeze up according to a honeycomb lattice when $\beta\to\infty$.