Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Violating conformal invariance: Two-dimensional clusters grafted to
  wedges, cones, and branch points of Riemann surfaces   We present simulations of 2-d site animals on square and triangular lattices
in non-trivial geomeLattice animals are one of the few critical models in
statistical mechanics violating conformal invariance. We present here
simulations of 2-d site animals on square and triangular lattices in
non-trivial geometries. The simulations are done with the newly developed PERM
algorithm which gives very precise estimates of the partition sum, yielding
precise values for the entropic exponent $\theta$ ($Z_N \sim \mu^N
N^{-\theta}$). In particular, we studied animals grafted to the tips of wedges
with a wide range of angles $\alpha$, to the tips of cones (wedges with the
sides glued together), and to branching points of Riemann surfaces. The latter
can either have $k$ sheets and no boundary, generalizing in this way cones to
angles $\alpha > 360$ degrees, or can have boundaries, generalizing wedges. We
find conformal invariance behavior, $\theta \sim 1/\alpha$, only for small
angles ($\alpha \ll 2\pi$), while $\theta \approx const -\alpha/2\pi$ for
$\alpha \gg 2\pi$. These scalings hold both for wedges and cones. A heuristic
(non-conformal) argument for the behavior at large $\alpha$ is given, and
comparison is made with critical percolation.

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The categories of this paper are: eess
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The categories of this paper are: hep-ex
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The categories of this paper are: nlin
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The categories of this paper are: solv-int
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The categories of this paper are: astro-ph
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The categories of this paper are: bayes-an
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The categories of this paper are: comp-gas
2
The categories of this paper are: math
29
The categories of this paper are: funct-an
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The categories of this paper are: econ
3
The categories of this paper are: physics
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The categories of this paper are: plasm-ph
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The categories of this paper are: alg-geom
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The categories of this paper are: acc-phys
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The categories of this paper are: q-fin
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The categories of this paper are: hep-lat