Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Probability of Incipient Spanning Clusters in Critical Square Bond
  Percolation   The probability of simultaneous occurence of at least k spanning clusters has
been studied by Monte Carlo simulations on the 2D square lattice at the bond
percolation threshold $p_c=1/2$. It is found that the probability of k and more
Incipient Spanning Clusters (ISC) has the values $P(k>1) \approx 0.00658(3)$
and $P(k>2) \approx 0.00000148(21)$ provided that the limit of these
probabilities for infinite lattices exists. The probability $P(k>3)$ of more
than three ISC could be estimated to be of the order of 10^{-11} and is beyond
the possibility to compute a such value by nowdays computers. So, it is
impossible to check in simulations the Aizenman law for the probabilities when
$k>>1$. We have detected a single sample with 4 ISC in a total number of about
10^{10} samples investigated. The probability of single event is 1/10 for that
number of samples.

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The categories of this paper are: nucl-ex
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The categories of this paper are: nlin
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The categories of this paper are: dg-ga
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The categories of this paper are: eess
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The categories of this paper are: cmp-lg
1
The categories of this paper are: cs
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The categories of this paper are: patt-sol
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The categories of this paper are: quant-ph
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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: physics
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The categories of this paper are: funct-an
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The categories of this paper are: q-alg
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The categories of this paper are: nucl-th
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The categories of this paper are: plasm-ph
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The categories of this paper are: comp-gas