Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: First-Order Vortex Lattice Melting and Magnetization of
  YBa$_2$Cu$_3$O$_{7-\delta}   We present the first non-mean-field calculation of the magnetization $M(T)$
of YBa$_2$Cu$_3$O$_{7-\delta}$ both above and below the flux-lattice melting
temperature $T_m(H)$. The results are in good agreement with experiment as a
function of transverse applied field $H$. The effects of fluctuations in both
order parameter $\psi({\bf r})$ and magnetic induction $B$ are included in the
Ginzburg-Landau free energy functional: $\psi({\bf r})$ fluctuates within the
lowest Landau level in each layer, while $B$ fluctuates uniformly according to
the appropriate Boltzmann factor. The second derivative $(\partial^2 M/\partial
T^2)_H$ is predicted to be negative throughout the vortex liquid state and
positive in the solid state. The discontinuities in entropy and magnetization
at melting are calculated to be $\sim 0.034\, k_B$ per flux line per layer and
$\sim 0.0014$~emu~cm$^{-3}$ at a field of 50 kOe.

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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: chao-dyn
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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: acc-phys
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The categories of this paper are: cmp-lg
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The categories of this paper are: q-bio
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The categories of this paper are: bayes-an
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The categories of this paper are: adap-org
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The categories of this paper are: chem-ph
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The categories of this paper are: hep-ph
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The categories of this paper are: atom-ph
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The categories of this paper are: funct-an
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The categories of this paper are: physics
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The categories of this paper are: hep-ex