Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Phase transition and thermodynamical geometry for Schwarzschild AdS
  black hole in $AdS_5\times{S^5}$ spacetime   We study thermodynamics and thermodynamic geometry of a five-dimensional
Schwarzschild AdS black hole in $AdS_5\times{S^5}$ spacetime by treating the
cosmological constant as the number of colors in the boundary gauge theory and
its conjugate quantity as the associated chemical potential. It is found that
the chemical potential is always negative in the stable branch of black hole
thermodynamics and it has a chance to be positive, but appears in the unstable
branch. We calculate scalar curvatures of the thermodynamical Weinhold metric,
Ruppeiner metric and Quevedo metric, respectively and we find that the
divergence of scalar curvature is related to the divergence of specific heat
with fixed chemical potential in the Weinhold metric and Ruppeiner metric,
while in the Quevedo metric the divergence of scalar curvature is related to
the divergence of specific heat with fixed number of colors and the vanishing
of the specific heat with fixed chemical potential.

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The categories of this paper are: cond-mat
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The categories of this paper are: nlin
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The categories of this paper are: alg-geom
3
The categories of this paper are: physics
1
The categories of this paper are: cs
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The categories of this paper are: hep-ex
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The categories of this paper are: math-ph
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The categories of this paper are: hep-lat
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The categories of this paper are: econ
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The categories of this paper are: q-fin
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The categories of this paper are: mtrl-th
36
The categories of this paper are: cmp-lg
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The categories of this paper are: astro-ph
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The categories of this paper are: nucl-ex
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The categories of this paper are: nucl-th
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The categories of this paper are: supr-con