Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Phase diagram of ferroelectrics with tricritical and Lifshitz points at
  coupling between polar and antipolar fluctuations   Static and dynamic critical behavior of Sn$_2$P$_2$S$_6$ type ferroelectrics
and (Pb$_y$Sn$_{1-y}$)$_2$P$_2$(Se$_x$S$_{1-x}$)$_6$ mixed crystals with line
of tricritical points and line of Lifshitz points on the $T-x-y$ phase diagram,
which meet at the tricritical Lifshitz point, can be described in a combined
BEG-ANNNI model. Such the model considers first and second neighbor
interactions for pseudospins in a local three-well potential. Below the
temperature of tricritical Lifshitz point, the "chaotic" state accompanied by
the coexistence of ferroelectric, metastable paraelectric and modulated phases
is expected. In addition to the frustration of polar fluctuations near the
Brillouin zone center, in Sn$_2$P$_2$S$_6$ crystal the antipolar fluctuations
also strongly develop in the paraelectric phase at cooling to continuous phase
transition temperature $T_0$. Here, critical behavior can be described as a
crossover between Ising and XY universality classes, what is expected near
bicritical points with coupled polar and antipolar order parameters and
competing instabilities in $q$-space.

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The categories of this paper are: adap-org
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The categories of this paper are: hep-ph
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The categories of this paper are: q-bio
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The categories of this paper are: eess
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The categories of this paper are: q-alg
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The categories of this paper are: q-fin
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The categories of this paper are: alg-geom
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The categories of this paper are: math-ph
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The categories of this paper are: nucl-ex
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The categories of this paper are: cmp-lg
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The categories of this paper are: econ
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The categories of this paper are: patt-sol
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The categories of this paper are: atom-ph
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The categories of this paper are: stat
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The categories of this paper are: hep-ex
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The categories of this paper are: nlin