Long Range Magnetic Order and the Darwin Lagrangian

TL;DR

This paper investigates the effects of Darwin magnetic interactions on confined electron systems, revealing phase transitions between static Wigner lattices and kinetic energy states, influenced by density, confinement, and dimensionality.

Contribution

It introduces a simulation approach incorporating Darwin magnetic interactions to study ground states of confined electrons in various dimensions and confinement potentials.

Findings

Below a critical density, electrons form a static Wigner lattice.

Above the critical density, the ground state has non-zero kinetic energy.

Confinement type and dimensionality affect the ground state structure.

Abstract

We simulate a finite system of $N$ confined electrons with inclusion of the Darwin magnetic interaction in two- and three-dimensions. The lowest energy states are located using the steepest descent quenching adapted for velocity dependent potentials. Below a critical density the ground state is a static Wigner lattice. For supercritical density the ground state has a non-zero kinetic energy. The critical density decreases with $N$ for exponential confinement but not for harmonic confinement. The lowest energy state also depends on the confinement and dimension: an antiferromagnetic cluster forms for harmonic confinement in two dimensions.