Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Fractal Behavior of the Shortest Path Between Two Lines in Percolation
  Systems   Using Monte-Carlo simulations, we determine the scaling form for the
probability distribution of the shortest path, $\ell$, between two lines in a
3-dimensional percolation system at criticality; the two lines can have
arbitrary positions, orientations and lengths. We find that the probability
distributions can exhibit up to four distinct power law regimes (separated by
cross-over regimes) with exponents depending on the relative orientations of
the lines. We explain this rich fractal behavior with scaling arguments.

12
The categories of this paper are: nucl-th
27
The categories of this paper are: comp-gas
13
The categories of this paper are: quant-ph
3
The categories of this paper are: physics
6
The categories of this paper are: astro-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: gr-qc
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The categories of this paper are: q-alg
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The categories of this paper are: stat
2
The categories of this paper are: math
28
The categories of this paper are: alg-geom
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The categories of this paper are: econ
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The categories of this paper are: solv-int
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The categories of this paper are: chem-ph
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The categories of this paper are: dg-ga