Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Directed Spiral Percolation Hull on the Square and Triangular Lattices   Critical properties of hulls of directed spiral percolation (DSP) clusters
are studied on the square and triangular lattices in two dimensions (2D). The
hull fractal dimension ($d_H$) and some of the critical exponents associated
with different moments of the hull size distribution function of the
anisotropic DSP clusters are reported here. The values of $d_H$ and other
critical exponents are found the same within error bars on both the lattices.
The universality of the hull's critical exponents then holds true between the
square and triangular lattices in 2D unlike the cluster's critical exponents
which exhibit a breakdown of universality. The hull fractal dimension $(d_H
\approx 1.46)$ is also found close to 4/3 and away from 7/4, that of ordinary
percolation cluster hull. A new conjecture is proposed for the hull fractal
dimension ($d_H$) in terms of two connectivity length exponents ($\nu_\|$ $&$
$\nu_\perp$) of the anisotropic clusters generated here. The values of $d_H$
and other critical exponents obtained here are very close to that of the spiral
percolation cluster hull. The hull properties of the DSP clusters are then
mostly determined by the rotational constraint and almost independent on the
directional constraint present in the model.

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The categories of this paper are: alg-geom
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The categories of this paper are: q-alg
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The categories of this paper are: comp-gas
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The categories of this paper are: hep-ph
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The categories of this paper are: acc-phys
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The categories of this paper are: nlin
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The categories of this paper are: cmp-lg
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The categories of this paper are: supr-con
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The categories of this paper are: ao-sci
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The categories of this paper are: patt-sol
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The categories of this paper are: math
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The categories of this paper are: nucl-th
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The categories of this paper are: mtrl-th
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The categories of this paper are: nucl-ex
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The categories of this paper are: quant-ph
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The categories of this paper are: chem-ph