Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Completely packed O($n$) loop models and their relation with exactly
  solved coloring models   We explore the physical properties of the completely packed O($n$) loop model
on the square lattice, and its generalization to an Eulerian graph model, which
follows by including cubic vertices which connect the four incoming loop
segments. This model includes crossing bonds as well. Our study of the
properties of this model involve transfer-matrix calculations and finite-size
scaling. The numerical results are compared to existing exact solutions,
including solutions of special cases of a so-called coloring model, which are
shown to be equivalent with our generalized loop model. The latter exact
solutions correspond with seven one-dimensional branches in the parameter space
of our generalized loop model. One of these branches, describing the case of
nonintersecting loops, is already known to correspond with the ordering
transition of the Potts model. We find that another exactly solved branch,
which describes a model with nonintersecting loops and cubic vertices,
corresponds with a first-order Ising-like phase transition for $n>2$. For
$1<n<2$, this branch can be interpreted in terms of a low-temperature O($n$)
phase with corner-cubic anisotropy. For $n>2$ this branch is the locus of a
first-order phase boundary between a phase with a hard-square lattice-gas like
ordering, and a phase dominated by cubic vertices. The first-order character of
this transition is in agreement with a mean-field argument.

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The categories of this paper are: bayes-an
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The categories of this paper are: supr-con
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The categories of this paper are: alg-geom
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The categories of this paper are: hep-th
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The categories of this paper are: comp-gas
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The categories of this paper are: nucl-th
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The categories of this paper are: nucl-ex
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The categories of this paper are: dg-ga
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The categories of this paper are: q-alg
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The categories of this paper are: ao-sci
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The categories of this paper are: physics
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The categories of this paper are: funct-an
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The categories of this paper are: math-ph
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The categories of this paper are: adap-org
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The categories of this paper are: nlin
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The categories of this paper are: cmp-lg