Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Gibbs measures of the Ising model with mixed spin-1 and spin-1/2 on a
  Cayley tree   In the present paper, the Ising model with mixed spin-(1,1/2) is considered
on the second order Cayley tree. A construction of splitting Gibbs measures
corresponding the model is given which allows to establish the existence of the
phase transition (non-uniqueness of Gibbs measures). We point out that, in the
phase transition region, the considered model has three translation-invariant
Gibbs measures in the ferromagnetic and anti-ferromagnetic regimes, while the
classical Ising model does not possesses such Gibbs measures in the
anti-ferromagnetic regime. It turns out that the considered model, like the
Ising model, exhibits a disordered Gibbs measure. Therefore, non-extremity and
extremity of such disordered Gibbs measures is investigated by means of
tree-indexed Markov chains.

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The categories of this paper are: acc-phys
5
The categories of this paper are: gr-qc
18
The categories of this paper are: econ
8
The categories of this paper are: hep-ex
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The categories of this paper are: nlin
6
The categories of this paper are: astro-ph
17
The categories of this paper are: q-fin
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The categories of this paper are: hep-th
0
The categories of this paper are: hep-ph
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The categories of this paper are: q-alg
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The categories of this paper are: nucl-ex
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The categories of this paper are: solv-int
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The categories of this paper are: eess
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The categories of this paper are: chao-dyn
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The categories of this paper are: cmp-lg
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The categories of this paper are: quant-ph