Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Phase transitions in Delaunay Potts models   We establish phase transitions for classes of continuum Delaunay multi-type
particle systems (continuum Potts models) with infinite range repulsive
interaction between particles of different type. In one class of the Delaunay
Potts models studied the repulsive interaction is a triangle (multi-body)
interaction whereas in the second class the interaction is between pairs
(edges) of the Delaunay graph. The result for the edge model is an extension of
finite range results in \cite{BBD04} for the Delaunay graph and in \cite{GH96}
for continuum Potts models to an infinite range repulsion decaying with the
edge length. This is a proof of an old conjecture of Lebowitz and Lieb. The
repulsive triangle interactions have infinite range as well and depend on the
underlying geometry and thus are a first step towards studying phase
transitions for geometry-dependent multi-body systems. Our approach involves a
Delaunay random-cluster representation analogous to the Fortuin-Kasteleyn
representation of the Potts model. The phase transitions manifest themselves in
the percolation of the corresponding random-cluster model. Our proofs rely on
recent studies \cite{DDG12} of Gibbs measures for geometry-dependent
interactions.

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The categories of this paper are: gr-qc
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The categories of this paper are: mtrl-th
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The categories of this paper are: plasm-ph
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The categories of this paper are: cs
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The categories of this paper are: hep-lat
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The categories of this paper are: atom-ph
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The categories of this paper are: hep-ph
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The categories of this paper are: q-alg
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The categories of this paper are: econ
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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: ao-sci
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The categories of this paper are: nucl-ex
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The categories of this paper are: adap-org
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The categories of this paper are: acc-phys
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The categories of this paper are: quant-ph