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Long Range Magnetic Order and the Darwin Lagrangian

Vishal Mehra·Jayme De Luca
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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.

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Vishal Mehra, Jayme De Luca. 1999-09-02. Long Range Magnetic Order and the Darwin Lagrangian. https://doi.org/10.1103/physreve.61.1199

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