Long Range Magnetic Order and the Darwin Lagrangian

Details Long Range Magnetic Order and the Darwin Lagrangian Long Range Magnetic Order and the Darwin Lagrangian

1999-09-02

arxiv.org/abs/cond-mat/9909030v1

Physics

Condensed Matter

Statistical Mechanics

5 figures

Scientific paper

10.1103/PhysRevE.61.1199

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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