Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Classification of point-group-symmetric orientational ordering tensors   The concept of symmetry breaking has been a propelling force in understanding
phases of matter. While rotational symmetry breaking is one of the most
prevalent examples, the rich landscape of orientational orders breaking the
rotational symmetries of isotropic space, i.e. $O(3)$, to a three-dimensional
point group remain largely unexplored, apart from simple examples such as
ferromagnetic or uniaxial nematic ordering. Here we provide an explicit
construction, utilizing a recently introduced gauge theoretical framework, to
address the three-dimensional point-group-symmetric orientational orders on a
general footing. This unified approach allows us to enlist order parameter
tensors for all three dimensional point groups. By construction, these tensor
order parameters are the minimal set of simplest tensors allowed by the
symmetries that uniquely characterize the orientational order. We explicitly
give these for the point groups $\{C_n, D_n, T, O, I\} \subset SO(3)$ and
$\{C_{nv}, S_n, C_{nh}, D_{nh}, D_{nd}, T_h, T_d, O_h, I_h\}\subset O(3)$ for
$n=\{1,2,3,4,6, \infty\}$. This central result may be perceived as a roadmap
for identifying exotic orientational orders that may become more and more in
reach in view of rapid experimental progress in e.g. nano-colloidal systems and
novel magnets.

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The categories of this paper are: bayes-an
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The categories of this paper are: comp-gas
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The categories of this paper are: atom-ph
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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: cmp-lg
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The categories of this paper are: eess
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The categories of this paper are: nucl-th
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The categories of this paper are: hep-lat
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The categories of this paper are: cs
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The categories of this paper are: supr-con
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The categories of this paper are: funct-an
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The categories of this paper are: chem-ph
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The categories of this paper are: gr-qc
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The categories of this paper are: chao-dyn
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The categories of this paper are: physics