Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Replica trick with real replicas: A way to build in thermodynamic
  homogeneity   We use real replicas to investigate stability of thermodynamic homogeneity of
the free energy of the Sherrington-Kirkpatrick (SK) model of spin glasses.
Within the replica trick with the replica symmetric ansatz we show that the
averaged free energy at low temperatures is not thermodynamically homogeneous.
The demand of minimization of the inhomogeneity of thermodynamic potentials
leads in a natural way to the hierarchical solution of the Parisi type.
Conditions for the global thermodynamic homogeneity are derived and evaluated
for the SK and $p$-spin infinite range models.

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The categories of this paper are: bayes-an
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The categories of this paper are: hep-ex
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The categories of this paper are: hep-lat
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The categories of this paper are: nucl-ex
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The categories of this paper are: q-alg
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The categories of this paper are: adap-org
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The categories of this paper are: solv-int
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The categories of this paper are: gr-qc
12
The categories of this paper are: nucl-th
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The categories of this paper are: mtrl-th
2
The categories of this paper are: math
20
The categories of this paper are: acc-phys
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The categories of this paper are: ao-sci
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The categories of this paper are: supr-con
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The categories of this paper are: math-ph
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The categories of this paper are: econ