Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Three-state Majority-Vote Model on Barab\'asi-Albert and Cubic Networks
  and the Unitary Relation for Critical Exponents   We investigate the three-state majority-vote model with noise on scale-free
and regular networks. In this model, an individual selects an opinion equal to
the opinion of the majority of its neighbors with probability $1 - q$ and
opposite to it with probability $q$. The parameter $q$ is called the noise
parameter of the model. We build a network of interactions where $z$ neighbors
are selected by each added site in the system, yielding a preferential
attachment network with degree distribution $k^{-\lambda}$, where $\lambda \sim
3$. In this work, $z$ is called growth parameter. Using finite-size scaling
analysis, we show that the critical exponents associated with the magnetization
and magnetic susceptibility add up to unity when a volumetric scaling is used,
regardless of the dimension of the network of interactions. Using Monte Carlo
simulations, we calculate the critical noise parameter $q_c$ as a function of
$z$ for the scale-free networks and obtain the phase diagram of the model. We
find that the critical noise is an increasing function of the growth parameter
$z$, and we define and verify numerically the unitary relation $\upsilon$ for
the critical exponents by calculating $\beta /\bar\nu$, $\gamma /\bar\nu$ and
$1/\bar\nu$ for several values of the network parameter $z$. We also obtain the
critical noise and the critical exponents for the two and three-state
majority-vote model on cubic lattices networks where we illustrate the
application of the unitary relation with a volumetric scaling.

19
The categories of this paper are: eess
27
The categories of this paper are: comp-gas
7
The categories of this paper are: hep-th
21
The categories of this paper are: adap-org
18
The categories of this paper are: econ
6
The categories of this paper are: astro-ph
29
The categories of this paper are: funct-an
37
The categories of this paper are: supr-con
12
The categories of this paper are: nucl-th
17
The categories of this paper are: q-fin
5
The categories of this paper are: gr-qc
1
The categories of this paper are: cs
16
The categories of this paper are: stat
34
The categories of this paper are: chem-ph
31
The categories of this paper are: ao-sci
9
The categories of this paper are: nlin