Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Extremality of translation-invariant Gibbs measures for the Potts-SOS
  model on the Cayley tree   In this paper, we consider the Potts-SOS model where the spin takes values in
the set $\{0, 1, 2\}$ on the Cayley tree of order two. We describe all the
translation-invariant splitting Gibbs measures for this model in some
conditions. Moreover, we investigate whether these Gibbs measures are extremal
or non-extremal in the set of all Gibbs measures.

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The categories of this paper are: nlin
29
The categories of this paper are: funct-an
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The categories of this paper are: nucl-ex
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The categories of this paper are: alg-geom
26
The categories of this paper are: bayes-an
8
The categories of this paper are: hep-ex
18
The categories of this paper are: econ
37
The categories of this paper are: supr-con
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The categories of this paper are: dg-ga
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The categories of this paper are: hep-lat
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The categories of this paper are: chao-dyn
35
The categories of this paper are: mtrl-th
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The categories of this paper are: hep-ph
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The categories of this paper are: atom-ph
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The categories of this paper are: gr-qc
30
The categories of this paper are: q-alg