Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Long Range Magnetic Order and the Darwin Lagrangian   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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The categories of this paper are: comp-gas
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The categories of this paper are: alg-geom
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The categories of this paper are: plasm-ph
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The categories of this paper are: math-ph
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The categories of this paper are: eess
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The categories of this paper are: chem-ph
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The categories of this paper are: astro-ph
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The categories of this paper are: hep-ex
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The categories of this paper are: hep-ph
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The categories of this paper are: q-alg
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The categories of this paper are: hep-th
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The categories of this paper are: nucl-ex
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The categories of this paper are: math
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The categories of this paper are: q-fin
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The categories of this paper are: bayes-an
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The categories of this paper are: hep-lat