Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Phase separation in the one-dimensional Hubbard model   The Hartree-Fock ground-state phase diagram of the one-dimensional Hubbard
model is calculated in the $\mu-U$ plane, restricted to phases with no charge
density modulation, extending the results presented in cond-mat/9511116. This
allows antiferromagnetism, saturated ferromagnetism, spiral spin density waves
and a collinear structure with unit cell $\uparrow \uparrow \downarrow
\downarrow$. The spiral phase is unstable against phase separation near
quarter-, half- and three-quarter-filling. For large $U$ this occurs at hole
(or electron) doping of $(3t/\pi^{2}U)^{1/3}$ from half filling.

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The categories of this paper are: adap-org
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The categories of this paper are: q-alg
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The categories of this paper are: gr-qc
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The categories of this paper are: q-bio
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The categories of this paper are: cmp-lg
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The categories of this paper are: hep-lat
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The categories of this paper are: ao-sci
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The categories of this paper are: funct-an
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The categories of this paper are: math
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The categories of this paper are: patt-sol
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The categories of this paper are: plasm-ph
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The categories of this paper are: stat
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The categories of this paper are: cs
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The categories of this paper are: dg-ga
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The categories of this paper are: math-ph
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The categories of this paper are: hep-ex