Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: On monochromatic arm exponents for 2D critical percolation   We investigate the so-called monochromatic arm exponents for critical
percolation in two dimensions. These exponents, describing the probability of
observing j disjoint macroscopic paths, are shown to exist and to form a
different family from the (now well understood) polychromatic exponents. More
specifically, our main result is that the monochromatic j-arm exponent is
strictly between the polychromatic j-arm and (j+1)-arm exponents.

7
The categories of this paper are: hep-th
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The categories of this paper are: hep-ph
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The categories of this paper are: chao-dyn
21
The categories of this paper are: adap-org
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The categories of this paper are: math-ph
19
The categories of this paper are: eess
3
The categories of this paper are: physics
29
The categories of this paper are: funct-an
32
The categories of this paper are: atom-ph
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The categories of this paper are: ao-sci
25
The categories of this paper are: patt-sol
33
The categories of this paper are: plasm-ph
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The categories of this paper are: hep-lat
12
The categories of this paper are: nucl-th
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The categories of this paper are: nlin
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The categories of this paper are: cmp-lg