Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Microscopic Derivation of Ginzburg-Landau Theory and the BCS Critical
  Temperature Shift in a Weak Homogeneous Magnetic Field   Starting from the Bardeen-Cooper-Schrieffer (BCS) free energy functional, we
derive the Ginzburg-Landau functional for the case of a weak homogeneous
magnetic field. We also provide an asymptotic formula for the BCS critical
temperature as a function of the magnetic field. This extends the previous
works arXiv:1102.4001 and arXiv:1410.2352 of Frank, Hainzl, Seiringer and
Solovej to the case of external magnetic fields with non-vanishing magnetic
flux through the unit cell.

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The categories of this paper are: gr-qc
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The categories of this paper are: alg-geom
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The categories of this paper are: solv-int
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The categories of this paper are: nlin
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The categories of this paper are: cmp-lg
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The categories of this paper are: physics
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The categories of this paper are: bayes-an
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The categories of this paper are: q-alg
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The categories of this paper are: econ
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The categories of this paper are: plasm-ph
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The categories of this paper are: comp-gas
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The categories of this paper are: nucl-th
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The categories of this paper are: funct-an
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The categories of this paper are: chao-dyn
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The categories of this paper are: hep-lat
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The categories of this paper are: q-bio