Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Thermodynamics of the Farey Fraction Spin Chain   We consider the Farey fraction spin chain, a one-dimensional model defined on
(the matrices generating) the Farey fractions. We extend previous work on the
thermodynamics of this model by introducing an external field $h$. From
rigorous and renormalization group arguments, we determine the phase diagram
and phase transition behavior of the extended model. Our results are fully
consistent with scaling theory (for the case when a "marginal" field is
present) despite the unusual nature of the transition for h=0.

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The categories of this paper are: q-bio
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The categories of this paper are: hep-lat
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The categories of this paper are: atom-ph
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The categories of this paper are: eess
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The categories of this paper are: hep-th
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The categories of this paper are: comp-gas
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The categories of this paper are: nucl-ex
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The categories of this paper are: funct-an
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The categories of this paper are: cmp-lg
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The categories of this paper are: hep-ex
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The categories of this paper are: hep-ph
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The categories of this paper are: cs
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The categories of this paper are: acc-phys
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The categories of this paper are: stat
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The categories of this paper are: alg-geom
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The categories of this paper are: patt-sol