Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Generalized Random Energy Models in a Transversal Magnetic Field: Free
  Energy and Phase Diagrams   We determine explicit variational expressions for the free energy of
mean-field spin glasses in a transversal magnetic field, whose glass
interaction is given by a hierarchical Gaussian potential as in Derrida's
Generalized Random Energy Model (GREM), its continuous version (CREM) or the
non-hierarchical GREM. The corresponding phase diagrams, which generally
include glass transitions as well as magnetic transitions, are discussed. In
the glass phase, the free energy is generally determined by both the parameters
of the classical model and the transversal field.

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The categories of this paper are: cs
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The categories of this paper are: astro-ph
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The categories of this paper are: eess
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The categories of this paper are: gr-qc
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The categories of this paper are: dg-ga
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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: plasm-ph
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The categories of this paper are: solv-int
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The categories of this paper are: nucl-th
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The categories of this paper are: nucl-ex
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The categories of this paper are: bayes-an
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The categories of this paper are: alg-geom
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The categories of this paper are: atom-ph
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The categories of this paper are: q-fin
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The categories of this paper are: econ