Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Critical frontier of the Potts and percolation models in triangular-type
  and kagome-type lattices I: Closed-form expressions   We consider the Potts model and the related bond, site, and mixed site-bond
percolation problems on triangular-type and kagome-type lattices, and derive
closed-form expressions for the critical frontier. For triangular-type lattices
the critical frontier is known, usually derived from a duality consideration in
conjunction with the assumption of a unique transition. Our analysis, however,
is rigorous and based on an established result without the need of a uniqueness
assumption, thus firmly establishing all derived results. For kagome-type
lattices the exact critical frontier is not known. We derive a closed-form
expression for the Potts critical frontier by making use of a homogeneity
assumption. The closed-form expression is new, and we apply it to a host of
problems including site, bond, and mixed site-bond percolation on various
lattices. It yields exact thresholds for site percolation on kagome, martini,
and other lattices, and is highly accurate numerically in other applications
when compared to numerical determination.

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The categories of this paper are: econ
25
The categories of this paper are: patt-sol
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The categories of this paper are: q-fin
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The categories of this paper are: acc-phys
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The categories of this paper are: eess
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The categories of this paper are: q-alg
1
The categories of this paper are: cs
9
The categories of this paper are: nlin
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The categories of this paper are: atom-ph
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The categories of this paper are: hep-lat
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The categories of this paper are: hep-ex
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The categories of this paper are: stat
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The categories of this paper are: nucl-th
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The categories of this paper are: q-bio
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The categories of this paper are: mtrl-th
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The categories of this paper are: dg-ga