Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Bond percolation on isoradial graphs: criticality and universality   In an investigation of percolation on isoradial graphs, we prove the
criticality of canonical bond percolation on isoradial embeddings of planar
graphs, thus extending celebrated earlier results for homogeneous and
inhomogeneous square, triangular, and other lattices. This is achieved via the
star-triangle transformation, by transporting the box-crossing property across
the family of isoradial graphs. As a consequence, we obtain the universality of
these models at the critical point, in the sense that the one-arm and
2j-alternating-arm critical exponents (and therefore also the connectivity and
volume exponents) are constant across the family of such percolation processes.
The isoradial graphs in question are those that satisfy certain weak conditions
on their embedding and on their track system. This class of graphs includes,
for example, isoradial embeddings of periodic graphs, and graphs derived from
rhombic Penrose tilings.

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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: patt-sol
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The categories of this paper are: acc-phys
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The categories of this paper are: q-bio
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The categories of this paper are: hep-ex
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The categories of this paper are: cs
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The categories of this paper are: plasm-ph
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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: astro-ph
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The categories of this paper are: hep-th
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The categories of this paper are: econ
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The categories of this paper are: eess
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The categories of this paper are: cmp-lg
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The categories of this paper are: q-fin