Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Study of the order of the phase transition in pure U(1) gauge theory
  with Villain action   We address the question of the order of the deconfinement phase transition of
four dimensional U(1) lattice gauge theory. Simulations of the Z-gauge theory
dual to the Villain action on toroidal lattices up to lattice sizes of 28^4
give results consistent with both, a vanishing and a nonvanishing discontinuity
in the thermodynamic limit. A decision on the order of the phase transition
requires still larger lattice sizes.

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The categories of this paper are: hep-th
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The categories of this paper are: quant-ph
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The categories of this paper are: nlin
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The categories of this paper are: math-ph
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The categories of this paper are: mtrl-th
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The categories of this paper are: cond-mat
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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: stat
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The categories of this paper are: cmp-lg
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The categories of this paper are: eess
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The categories of this paper are: chao-dyn
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The categories of this paper are: comp-gas
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The categories of this paper are: econ
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The categories of this paper are: alg-geom
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The categories of this paper are: math