Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Solitonic spin-liquid state due to the violation of the Lifshitz
  condition in Fe$_{1+y}$Te   A combination of phenomenological analysis and M\"ossbauer spectroscopy
experiments on the tetragonal Fe$_{1+y}$Te system indicates that the magnetic
ordering transition in compounds with higher Fe-excess, $y\ge$ 0.11, is
unconventional. Experimentally, a liquid-like magnetic precursor with
quasi-static spin-order is found from significantly broadened M\"ossbauer
spectra at temperatures above the antiferromagnetic transition. The
incommensurate spin-density wave (SDW) order in Fe$_{1+y}$Te is described by a
magnetic free energy that violates the weak Lifshitz condition in the Landau
theory of second-order transitions. The presence of multiple Lifshitz
invariants provides the mechanism to create multidimensional, twisted, and
modulated solitonic phases.

5
The categories of this paper are: gr-qc
36
The categories of this paper are: cmp-lg
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The categories of this paper are: dg-ga
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The categories of this paper are: patt-sol
8
The categories of this paper are: hep-ex
13
The categories of this paper are: quant-ph
31
The categories of this paper are: ao-sci
17
The categories of this paper are: q-fin
9
The categories of this paper are: nlin
21
The categories of this paper are: adap-org
0
The categories of this paper are: hep-ph
22
The categories of this paper are: chao-dyn
10
The categories of this paper are: q-bio
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The categories of this paper are: hep-lat
14
The categories of this paper are: math-ph
28
The categories of this paper are: alg-geom