Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Pair approximation for the q-voter models with quenched disorder on
  networks   Using two models of opinion dynamics, the $q$-voter model with independence
and the $q$-voter model with anticonformity, we discuss how the change of
disorder from annealed to quenched affects phase transitions on networks. Up
till now, such an analysis has been done only at the mean-field level. To
derive phase diagrams on networks, we develop the pair approximation for the
quenched versions of the models. This formalism can be also applied to other
quenched dynamics of similar kind. The results indicate that such a change of
disorder eliminates all discontinuous phase transitions and broadens ordered
phases. We show that although the annealed and quenched types of disorder lead
to the same result in the $q$-voter model with anticonformity at the mean-field
level, they do lead to distinct phase diagrams on networks. These phase
diagrams shift towards each other as the average node degree of a network
increases, and eventually, they coincide in the mean-field limit. In contrast,
for the $q$-voter model with independence, the phase diagrams move towards the
same direction regardless of the disorder type, and they do not coincide even
in the mean-filed limit. To validate our results, we carry out Monte Carlo
simulations on random regular graphs and Barab\'{a}si-Albert networks. Although
the pair approximation may incorrectly predict the type of phase transitions
for the annealed models, we have not observed such errors for their quenched
counterparts.

12
The categories of this paper are: nucl-th
36
The categories of this paper are: cmp-lg
23
The categories of this paper are: solv-int
13
The categories of this paper are: quant-ph
28
The categories of this paper are: alg-geom
21
The categories of this paper are: adap-org
14
The categories of this paper are: math-ph
18
The categories of this paper are: econ
25
The categories of this paper are: patt-sol
24
The categories of this paper are: dg-ga
0
The categories of this paper are: hep-ph
37
The categories of this paper are: supr-con
5
The categories of this paper are: gr-qc
31
The categories of this paper are: ao-sci
29
The categories of this paper are: funct-an
9
The categories of this paper are: nlin