Minimum energy configurations of repelling particles in two dimensions

TL;DR

This paper investigates the minimal energy arrangements of identical repelling particles in two dimensions, analyzing various interaction potentials, stability of triangular structures, and the emergence of alternative configurations, with implications for three-dimensional systems.

Contribution

It introduces a comprehensive analysis of geometrical arrangements for repelling particles, including stability conditions and the discovery of alternative structures beyond the triangular lattice.

Findings

Triangular lattice stability conditions derived.

Alternative structures with non-trivial unit cells identified.

Qualitative behavior expected to extend to three dimensions.

Abstract

Geometrical arrangements of minimum energy of a system of identical repelling particles in two dimensions are studied for different forms of the interaction potential. Stability conditions for the triangular structure are derived, and some potentials not satisfying them are discussed. It is shown that in addition to the triangular lattice, other structures may appear (some of them with non-trivial unit cells, and non-equivalent positions of the particles) even for simple choices of the interaction. The same qualitative behavior is expected in three dimensions.