  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.
