Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Phase transition in the diffusion and bootstrap percolation models on
  regular random and Erd\H{o}s-R\'{e}nyi networks   The diffusion and bootstrap percolation models were studied in regular random
and Erd\H{o}s-R\'{e}nyi networks using the modified Newman-Ziff algorithms. We
calculated the percolation threshold and the order parameter of the percolation
transition (strength of the giant cluster) and its derivatives. The percolation
transitions are classified by the results. The diffusion percolation with a
small $k$ has a double transition, and the bootstrap percolation with $m\geq3$
has the first-order percolation transition. The diffusion percolation with a
large $k$ and the bootstrap percolation with a small $m$ show the second-order
percolation transition. Particularly, third-order percolation transitions were
discovered in the bootstrap percolation of $m=2$ in regular random networks.

25
The categories of this paper are: patt-sol
35
The categories of this paper are: mtrl-th
2
The categories of this paper are: math
0
The categories of this paper are: hep-ph
8
The categories of this paper are: hep-ex
24
The categories of this paper are: dg-ga
32
The categories of this paper are: atom-ph
21
The categories of this paper are: adap-org
7
The categories of this paper are: hep-th
30
The categories of this paper are: q-alg
19
The categories of this paper are: eess
12
The categories of this paper are: nucl-th
20
The categories of this paper are: acc-phys
10
The categories of this paper are: q-bio
13
The categories of this paper are: quant-ph
6
The categories of this paper are: astro-ph