Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Simple cubic random-site percolation thresholds for neighborhoods
  containing fourth-nearest neighbors   In the paper random-site percolation thresholds for simple cubic lattice with
sites' neighborhoods containing next-next-next-nearest neighbors (4NN) are
evaluated with Monte Carlo simulations. A recently proposed algorithm with low
sampling for percolation thresholds estimation [Bastas et al., arXiv:1411.5834]
is implemented for the studies of the top-bottom wrapping probability. The
obtained percolation thresholds are $p_C(\text{4NN})=0.31160(12)$,
$p_C(\text{4NN+NN})=0.15040(12)$, $p_C(\text{4NN+2NN})=0.15950(12)$,
$p_C(\text{4NN+3NN})=0.20490(12)$, $p_C(\text{4NN+2NN+NN})=0.11440(12)$,
$p_C(\text{4NN+3NN+NN})=0.11920(12)$, $p_C(\text{4NN+3NN+2NN})=0.11330(12)$,
$p_C(\text{4NN+3NN+2NN+NN})=0.10000(12)$, where 3NN, 2NN, NN stands for
next-next-nearest neighbors, next-nearest neighbors, and nearest neighbors,
respectively. As an SC lattice with 4NN neighbors may be mapped onto two
independent interpenetrated SC lattices but with two times larger lattice
constant the percolation threshold $p_C$(4NN) is exactly equal to $p_C$(NN).
The simplified Bastas et al. method allows for reaching uncertainty of the
percolation threshold value $p_C$ similar to those obtained with classical
method but ten times faster.

31
The categories of this paper are: ao-sci
25
The categories of this paper are: patt-sol
23
The categories of this paper are: solv-int
33
The categories of this paper are: plasm-ph
19
The categories of this paper are: eess
21
The categories of this paper are: adap-org
10
The categories of this paper are: q-bio
36
The categories of this paper are: cmp-lg
24
The categories of this paper are: dg-ga
12
The categories of this paper are: nucl-th
3
The categories of this paper are: physics
29
The categories of this paper are: funct-an
5
The categories of this paper are: gr-qc
0
The categories of this paper are: hep-ph
37
The categories of this paper are: supr-con
34
The categories of this paper are: chem-ph