Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Double-dimers, the Ising model and the hexahedron recurrence   We define and study a recurrence relation in ${\mathbb Z}^3$, called the
hexahedron recurrence, which is similar to the octahedron recurrence (Hirota
bilinear difference equation) and cube recurrence (Miwa equation). Like these
examples, solutions to the hexahedron recurrence are partition sums for edge
configurations on a certain graph, and have a natural interpretation in terms
of cluster algebras. We give an explicit correspondence between monomials in
the Laurent expansions arising in the recurrence with certain double-dimer
configurations of a graph. We compute limit shapes for the corresponding
double-dimer configurations.
  The Kashaev difference equation arising in the Ising model star-triangle
relation is a special case of the hexahedron recurrence. In particular this
reveals the cluster nature underlying the Ising model. The above relation
allows us to prove a Laurent phenomenon for the Kashaev difference equation.

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The categories of this paper are: cs
31
The categories of this paper are: ao-sci
33
The categories of this paper are: plasm-ph
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The categories of this paper are: bayes-an
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The categories of this paper are: gr-qc
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The categories of this paper are: nucl-ex
35
The categories of this paper are: mtrl-th
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The categories of this paper are: solv-int
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The categories of this paper are: econ
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The categories of this paper are: chao-dyn
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The categories of this paper are: physics
17
The categories of this paper are: q-fin
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The categories of this paper are: hep-lat
32
The categories of this paper are: atom-ph
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The categories of this paper are: astro-ph
20
The categories of this paper are: acc-phys