Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Phase Transitions in Mesoscopic Superconducting Films   We solve the Ginzburg-Landau equation (GLE) for the mesoscopic
superconducting thin film of the square shape in the magnetic field for the
wide range of the Ginzburg-Landau parameter $0.05<\kappa_{eff}<\infty $. We
found that the phase with the antivortex exists in the broad range of
parameters. When the coherence length decreases the topological phase
transition to the phase with the same total vorticity and a reduced symmetry
takes place. The giant vortex with the vorticity $m=3$ is found to be unstable
for any field, $\xi /a$ and $\kappa_{eff}\ge 0.1$. Reduction of $ \kappa
_{eff}$ does not make the phase with antivortex more stable contrary to the
case of the cylindric sample of the type I superconductor.

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The categories of this paper are: q-bio
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The categories of this paper are: stat
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The categories of this paper are: math
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The categories of this paper are: patt-sol
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The categories of this paper are: chem-ph
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The categories of this paper are: bayes-an
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The categories of this paper are: comp-gas
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The categories of this paper are: plasm-ph
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The categories of this paper are: funct-an
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The categories of this paper are: acc-phys
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The categories of this paper are: hep-ex
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The categories of this paper are: physics
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The categories of this paper are: nucl-ex
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The categories of this paper are: econ
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The categories of this paper are: eess
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The categories of this paper are: quant-ph