Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: On the Aizenman exponent in critical percolation   The probabilities of clusters spanning a hypercube of dimensions two to seven
along one axis of a percolation system under criticality were investigated
numerically. We used a modified Hoshen--Kopelman algorithm combined with
Grassberger's "go with the winner" strategy for the site percolation. We
carried out a finite-size analysis of the data and found that the probabilities
confirm Aizenman's proposal of the multiplicity exponent for dimensions three
to five. A crossover to the mean-field behavior around the upper critical
dimension is also discussed.

25
The categories of this paper are: patt-sol
1
The categories of this paper are: cs
35
The categories of this paper are: mtrl-th
29
The categories of this paper are: funct-an
26
The categories of this paper are: bayes-an
19
The categories of this paper are: eess
17
The categories of this paper are: q-fin
6
The categories of this paper are: astro-ph
34
The categories of this paper are: chem-ph
21
The categories of this paper are: adap-org
15
The categories of this paper are: nucl-ex
32
The categories of this paper are: atom-ph
7
The categories of this paper are: hep-th
24
The categories of this paper are: dg-ga
33
The categories of this paper are: plasm-ph
20
The categories of this paper are: acc-phys