Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Predictions of bond percolation thresholds for the kagom\'e and
  Archimedean $(3,12^2)$ lattices   Here we show how the recent exact determination of the bond percolation
threshold for the martini lattice can be used to provide approximations to the
unsolved kagom\'e and (3,12^2) lattices. We present two different methods, one
of which provides an approximation to the inhomogeneous kagom\'e and (3,12^2)
bond problems, and the other gives estimates of $p_c$ for the homogeneous
kagom\'e (0.5244088...) and (3,12^2) (0.7404212...) problems that respectively
agree with numerical results to five and six significant figures.

17
The categories of this paper are: q-fin
10
The categories of this paper are: q-bio
7
The categories of this paper are: hep-th
35
The categories of this paper are: mtrl-th
5
The categories of this paper are: gr-qc
26
The categories of this paper are: bayes-an
1
The categories of this paper are: cs
16
The categories of this paper are: stat
29
The categories of this paper are: funct-an
0
The categories of this paper are: hep-ph
25
The categories of this paper are: patt-sol
37
The categories of this paper are: supr-con
28
The categories of this paper are: alg-geom
36
The categories of this paper are: cmp-lg
9
The categories of this paper are: nlin
2
The categories of this paper are: math