Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: A new route to Explosive Percolation   The biased link occupation rule in the Achlioptas process (AP) discourages
the large clusters to grow much ahead of others and encourages faster growth of
clusters which lag behind. In this paper we propose a model where this tendency
is sharply reflected in the Gamma distribution of the cluster sizes, unlike the
power law distribution in AP. In this model single edges between pairs of
clusters of sizes $s_i$ and $s_j$ are occupied with a probability $\propto
(s_is_j)^{\alpha}$. The parameter $\alpha$ is continuously tunable over the
entire real axis. Numerical studies indicate that for $\alpha < \alpha_c$ the
transition is first order, $\alpha_c=0$ for square lattice and $\alpha_c=-1/2$
for random graphs. In the limits of $\alpha = -\infty, +\infty$ this model
coincides with models well established in the literature.

28
The categories of this paper are: alg-geom
33
The categories of this paper are: plasm-ph
22
The categories of this paper are: chao-dyn
20
The categories of this paper are: acc-phys
5
The categories of this paper are: gr-qc
35
The categories of this paper are: mtrl-th
23
The categories of this paper are: solv-int
18
The categories of this paper are: econ
34
The categories of this paper are: chem-ph
32
The categories of this paper are: atom-ph
15
The categories of this paper are: nucl-ex
0
The categories of this paper are: hep-ph
17
The categories of this paper are: q-fin
10
The categories of this paper are: q-bio
11
The categories of this paper are: hep-lat
31
The categories of this paper are: ao-sci