Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Frustrated spin-$\frac{1}{2}$ Heisenberg magnet on an $AA$-stacked
  honeycomb bilayer: High-order study of the collinear magnetic phases of the
  $J_{1}$--$J_{2}$--$J_{1}^{\perp}$ model   The zero-temperature phase diagram of the frustrated spin-$\frac{1}{2}$
$J_{1}$--$J_{2}$--$J_{1}^{\perp}$ Heisenberg magnet on an $AA$-stacked
honeycomb bilayer lattice is studied using the coupled cluster method
implemented to very high orders. On each monolayer the spins interact via
nearest-neighbor (NN) and frustrating next-nearest-neighbor isotropic
antiferromagnetic Heisenberg interactions with respective strength parameters
$J_{1}>0$ and $J_{2}\equiv\kappa J_{1}>0$. The two layers are coupled such that
NN interlayer pairs of spins also interact via a similar isotropic Heisenberg
interaction of strength $J_{1}^{\perp}\equiv \delta J_{1}$, which may be of
either sign. In particular, we locate with high accuracy the complete phase
boundaries in the $\kappa$-$\delta$ half-plane with $\kappa>0$ of the two
quasiclassical collinear antiferromagnetic phases with N\'{e}el or N\'{e}el-II
magnetic order in each monolayer, and the interlayer NN pairs of spins either
aligned (for $\delta<0$) or anti-aligned (for $\delta > 0$) to one another.
Compared to the two-sublattice N\'{e}el order, in which all NN intralayer pairs
of spins are antiparallel to one another, the four-sublattice N\'{e}el-II order
is characterized by NN intralayer pairs of spins on the honeycomb lattice being
antiparallel to one another along zigzag (or sawtooth) chains in a specified
direction from among the three equivalent honeycomb-lattice directions, and
parallel to one another for the corresponding interchain pairs.

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The categories of this paper are: math
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The categories of this paper are: math-ph
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The categories of this paper are: bayes-an
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The categories of this paper are: dg-ga
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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: plasm-ph
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The categories of this paper are: hep-th
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The categories of this paper are: mtrl-th
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The categories of this paper are: eess
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The categories of this paper are: atom-ph
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The categories of this paper are: physics
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The categories of this paper are: alg-geom
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The categories of this paper are: hep-ph
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The categories of this paper are: ao-sci
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The categories of this paper are: cs