Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: The Fr\"ohlich-Spencer Proof of the Berezinskii-Kosterlitz-Thouless
  Transition   We present the Fr\"ohlich-Spencer proof of the
Berezinskii-Kosterlitz-Thouless transition. Our treatment includes the proof of
delocalization for the integer-valued discrete Gaussian free field at high
temperature and the proof of existence of a phase with power-law decay of
correlations in the plane rotator model with Villain interaction, both in two
dimensions. The treatment differs from the original in various technical points
and we hope it will be of benefit to the community.

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The categories of this paper are: hep-th
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The categories of this paper are: supr-con
22
The categories of this paper are: chao-dyn
28
The categories of this paper are: alg-geom
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The categories of this paper are: nucl-th
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The categories of this paper are: astro-ph
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The categories of this paper are: q-fin
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The categories of this paper are: funct-an
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The categories of this paper are: solv-int
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The categories of this paper are: stat
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The categories of this paper are: econ
11
The categories of this paper are: hep-lat
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The categories of this paper are: comp-gas
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The categories of this paper are: nlin
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The categories of this paper are: hep-ph
13
The categories of this paper are: quant-ph