Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Two Geometric Approaches To Study The Deconfinement Phase Transition in
  (3+1)-Dimensional $Z_2$ Gauge Theories   We have simulated $(3+1)-$dimensional finite temperature $Z_2$ gauge theory
by using Metropolis algorithm. We aimed to observe the deconfinement phase
transitions by using geometric methods. In order to do so we have proposed two
different methods which can be applied to $3-$dimensional effective spin model
consisting of Polyakov loop variables. The first method is based on studies of
cluster structures of each configuration. For each temperature, configurations
are obtained from a set of bond probability ($P$) values. At a certain
probability, percolating clusters start to emerge. Unless the probability value
coincides with the Coniglio-Klein probability value, the fluctuations are less
than the actual fluctuations at the critical point. In this method the task is
to identify the probability value which yields the highest peak in the
diverging quantities on finite lattices. The second method uses the scaling
function based on the surface renormalization which is of geometric origin.
Since this function is a scaling function, the measurements done on
different-size lattices yield the same value at the critical point, apart from
the correction to scaling terms. The linearization of the scaling function
around the critical point yields the critical point and the critical exponents.

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The categories of this paper are: q-bio
35
The categories of this paper are: mtrl-th
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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: astro-ph
12
The categories of this paper are: nucl-th
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The categories of this paper are: hep-th
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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: q-alg
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The categories of this paper are: hep-ph
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The categories of this paper are: chao-dyn
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The categories of this paper are: bayes-an
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The categories of this paper are: stat
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The categories of this paper are: nucl-ex
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The categories of this paper are: cmp-lg