Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Crossover from mean-field to $2d$ Directed Percolation in the contact
  process   We study the contact process on spatially embedded networks, consisting of a
regular square lattice with long-range connections. To generate the networks, a
long-range connection is randomly added to each node $i$ of a square lattice,
following the probability, $P_{ij}\sim{r_{ij}^{-\alpha}}$ , where $r_{ij}$ is
the Manhattan distance between nodes $i$ and $j$, and the exponent $\alpha$ is
a tunable parameter. Extensive Monte Carlo simulations and a finite-size
scaling analysis for different values of $\alpha$ reveal a crossover from the
mean-field to $2d$ Directed Percolation universality class with increasing
$\alpha$, in the range $3<\alpha<4$.

12
The categories of this paper are: nucl-th
8
The categories of this paper are: hep-ex
10
The categories of this paper are: q-bio
28
The categories of this paper are: alg-geom
18
The categories of this paper are: econ
34
The categories of this paper are: chem-ph
31
The categories of this paper are: ao-sci
33
The categories of this paper are: plasm-ph
7
The categories of this paper are: hep-th
27
The categories of this paper are: comp-gas
22
The categories of this paper are: chao-dyn
5
The categories of this paper are: gr-qc
29
The categories of this paper are: funct-an
13
The categories of this paper are: quant-ph
9
The categories of this paper are: nlin
0
The categories of this paper are: hep-ph