Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Two Types of Discontinuous Percolation Transitions in Cluster Merging
  Processes   Percolation is a paradigmatic model in disordered systems and has been
applied to various natural phenomena. The percolation transition is known as
one of the most robust continuous transitions. However, recent extensive
studies have revealed that a few models exhibit a discontinuous percolation
transition (DPT) in cluster merging processes. Unlike the case of continuous
transitions, understanding the nature of discontinuous phase transitions
requires a detailed study of the system at hand, which has not been undertaken
yet for DPTs. Here we examine the cluster size distribution immediately before
an abrupt increase in the order parameter of DPT models and find that DPTs
induced by cluster merging kinetics can be classified into two types. Moreover,
the type of DPT can be determined by the key characteristic of whether the
cluster kinetic rule is homogeneous with respect to the cluster sizes. We also
establish the necessary conditions for each type of DPT, which can be used
effectively when the discontinuity of the order parameter is ambiguous, as in
the explosive percolation model.

28
The categories of this paper are: alg-geom
7
The categories of this paper are: hep-th
24
The categories of this paper are: dg-ga
14
The categories of this paper are: math-ph
2
The categories of this paper are: math
22
The categories of this paper are: chao-dyn
36
The categories of this paper are: cmp-lg
30
The categories of this paper are: q-alg
32
The categories of this paper are: atom-ph
5
The categories of this paper are: gr-qc
27
The categories of this paper are: comp-gas
20
The categories of this paper are: acc-phys
15
The categories of this paper are: nucl-ex
21
The categories of this paper are: adap-org
6
The categories of this paper are: astro-ph
17
The categories of this paper are: q-fin