Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Geometrical vs. Fortuin-Kasteleyn Clusters in the Two-Dimensional
  $q$-State Potts Model   The tricritical behavior of the two-dimensional $q$-state Potts model with
vacancies for $1\leq q \leq4$ is argued to be encoded in the fractal structure
of the geometrical spin clusters of the pure model. The close connection
between the critical properties of the pure model and the tricritical
properties of the diluted model is shown to be reflected in an intimate
relation between Fortuin-Kasteleyn and geometrical clusters: The same
transformation mapping the two critical regimes onto each other also maps the
two cluster types onto each other. The map conserves the central charge, so
that both cluster types are in the same universality class. The geometrical
picture is supported by a Monte Carlo simulation of the high-temperature
representation of the Ising model ($q=2$). In this new numerical approach,
closed graph configurations are generated by means of a Metropolis update
algorithm, involving single plaquettes.

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The categories of this paper are: ao-sci
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The categories of this paper are: atom-ph
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The categories of this paper are: eess
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The categories of this paper are: patt-sol
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The categories of this paper are: funct-an
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The categories of this paper are: mtrl-th
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The categories of this paper are: alg-geom
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The categories of this paper are: q-bio
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The categories of this paper are: hep-th
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The categories of this paper are: nlin
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The categories of this paper are: dg-ga
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The categories of this paper are: math-ph
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The categories of this paper are: supr-con
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The categories of this paper are: gr-qc
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The categories of this paper are: stat
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The categories of this paper are: comp-gas