Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Wigner crystallization in quantum electron bilayers   The phase diagram of quantum electron bilayers in zero magnetic field is
obtained using density functional theory. For large electron densities the
system is in the liquid phase, while for smaller densities the liquid may
freeze (Wigner crystallization) into four different crystalline phases; the
lattice symmetry and the critical density depend on the the inter-layer
distance. The phase boundaries between different Wigner crystals consist of
both first and second order transitions, depending on the phases involved, and
join the freezing curve at three different triple points.

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The categories of this paper are: patt-sol
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The categories of this paper are: acc-phys
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The categories of this paper are: nucl-th
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The categories of this paper are: dg-ga
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The categories of this paper are: physics
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The categories of this paper are: atom-ph
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The categories of this paper are: supr-con
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The categories of this paper are: math-ph
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The categories of this paper are: chao-dyn
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The categories of this paper are: alg-geom
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The categories of this paper are: ao-sci
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The categories of this paper are: solv-int
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The categories of this paper are: nlin
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The categories of this paper are: astro-ph
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The categories of this paper are: comp-gas
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The categories of this paper are: eess