Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Lagrangian formulation for emergent elastic waves in magnetic emergent
  crystals   Magnetic emergent crystals are periodic alignment of "particle-like" spin
textures that emerge in magnets. Instead of focusing on an individual spin or a
macroscopic magnetization field, we analyze the dynamical behaviors of these
novel states by taking a solid-state point of view. Based on variational
principles, the basic equations for lattice dynamics of any emergent
crystalline states appearing in magnetic materials is established. For small
amplitude emergent elastic waves propagating in emergent crystals, the basic
equations reduce to an eigenvalue problem, from which the dispersion relation
and vibrational patterns for all emergent phonons are determined at the long
wavelength limit.

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The categories of this paper are: ao-sci
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The categories of this paper are: q-bio
27
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: bayes-an
7
The categories of this paper are: hep-th
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The categories of this paper are: q-fin
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The categories of this paper are: stat
25
The categories of this paper are: patt-sol
13
The categories of this paper are: quant-ph
12
The categories of this paper are: nucl-th
0
The categories of this paper are: hep-ph
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The categories of this paper are: hep-lat
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The categories of this paper are: solv-int
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The categories of this paper are: dg-ga
2
The categories of this paper are: math