Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Renormalization group for link percolation on planar hyperbolic
  manifolds   Network geometry is currently a topic of growing scientific interest as it
opens the possibility to explore and interpret the interplay between structure
and dynamics of complex networks using geometrical arguments. However the field
is still in its infancy. In this work we investigate the role of network
geometry in determining the nature of the percolation transition in planar
hyperbolic manifolds. In Ref. [1], S. Boettcher, V. Singh, R. M. Ziff have
shown that a special type of two-dimensional hyperbolic manifolds, the Farey
graphs, display a discontinuous transition for ordinary link percolation. Here
using the renormalization group we investigate the critical properties of link
percolation on a wider class of two-dimensional hyperbolic deterministic and
random manifolds constituting the skeletons of two-dimensional cell complexes.
These hyperbolic manifolds are built iteratively by subsequently gluing
$m$-polygons to single edges. We show that when the size $m$ of the polygons is
drawn from a distribution $q_m$ with asymptotic power-law scaling $q_m\simeq
Cm^{-\gamma}$ for $m\gg1$, different universality classes can be observed for
different values of the power-law exponent $\gamma$. Interestingly the
percolation transition is hybrid for $\gamma\in (3,4)$ and becomes continuous
for $\gamma \in (2,3]$

14
The categories of this paper are: math-ph
18
The categories of this paper are: econ
11
The categories of this paper are: hep-lat
15
The categories of this paper are: nucl-ex
13
The categories of this paper are: quant-ph
33
The categories of this paper are: plasm-ph
36
The categories of this paper are: cmp-lg
1
The categories of this paper are: cs
27
The categories of this paper are: comp-gas
37
The categories of this paper are: supr-con
8
The categories of this paper are: hep-ex
35
The categories of this paper are: mtrl-th
34
The categories of this paper are: chem-ph
31
The categories of this paper are: ao-sci
2
The categories of this paper are: math
29
The categories of this paper are: funct-an