Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Extended Z-invariance for integrable vector and face models and
  multi-component integrable quad equations   In a previous paper, the author has established an extension of the
Z-invariance property for integrable edge-interaction models of statistical
mechanics, that satisfy the star-triangle relation (STR) form of the
Yang-Baxter equation (YBE). In the present paper, an analogous extended
Z-invariance property is shown to also hold for integrable vector models and
interaction-round-a-face (IRF) models of statistical mechanics respectively. As
for the previous case of the STR, the Z-invariance property is shown through
the use of local cubic-type deformations of a 2-dimensional surface associated
to the models, which allow an extension of the models onto a subset of next
nearest neighbour vertices of $\mathbb{Z}^3$, while leaving the partition
functions invariant. These deformations are permitted as a consequence of the
respective YBE's satisfied by the models. The quasi-classical limit is also
considered, and it is shown that an analogous Z-invariance property holds for
the variational formulation of classical discrete Laplace equations which arise
in this limit. From this limit, new integrable 3D-consistent multi-component
quad equations are proposed, which are constructed from a degeneration of the
equations of motion for IRF Boltzmann weights.

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The categories of this paper are: cmp-lg
24
The categories of this paper are: dg-ga
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The categories of this paper are: econ
23
The categories of this paper are: solv-int
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The categories of this paper are: eess
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The categories of this paper are: acc-phys
11
The categories of this paper are: hep-lat
32
The categories of this paper are: atom-ph
8
The categories of this paper are: hep-ex
30
The categories of this paper are: q-alg
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The categories of this paper are: chao-dyn
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The categories of this paper are: nucl-ex
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The categories of this paper are: funct-an
0
The categories of this paper are: hep-ph
6
The categories of this paper are: astro-ph
10
The categories of this paper are: q-bio