18-21 September 2019
Europe/Warsaw timezone

$q$-Neighbor Majority-Vote Model on Complex Networks

20 Sep 2019, 12:40


Talk Session 6


Andrzej Krawiecki (Faculty of Physics, Warsaw University of Technology)


A $q$-neighbor majority-vote model for the opinion formation is introduced in which agents
represented by two-state spins update their opinions on the basis of the opinions of
randomly chosen subsets of $q$ their neighbors ($q$-lobbies). The agents with probability
$(1-2p)$, $0\le p\le1/2$, obey the majority-vote
rule in which the probability of the opinion flip depends only on the sign of the resultant
opinion of the $q$-lobby, and with probability $2p$ act independently and change opinion or
remain in the actual state with equal probabilities. Thus, the parameter $p$ controls the
degree of stochasticity in the model. In the model under study the
agents are located in the nodes of complex networks, e.g., Erd\"os-R\'enyi graphs or
scale-free networks, and the neighborhood of each agent consists of all agents
connected with him/her by edges, out of which the $q$-lobby is chosen randomly at each
step of the Monte Carlo simulation. This model is related to a recently introduced
$q$-neighbor Ising model [A.\ J\c{e}drzejewski et al., Phys.\ Rev.\ E 92, 052105 (2015);
A.\ Chmiel et al., Int.\ J.\ Modern Phys.\ C 29, 1850041 (2018)], with agents obeying
Metropolis opinion update rule, in which, in particular, first-order ferromagnetic transition was
reported, with the width of the hysteresis loop oscillating with $q$. In contrast, in the
$q$-neighbor majority vote model only second-order ferromagnetic transition is observed.
Theory for this transition is presented both in the mean-field approximation, valid for
large mean degrees of nodes and large $q$, and in a more elaborate pair approximation. In the
latter case the predicted location of the critical point $p_{c}$ agrees quantitatively with that
obtained from Monte Carlo simulations for various complex networks with broad range of
mean degrees of nodes and sizes of the $q$-lobby. Finite size scaling analysis shows that
in the vicinity of the critical point the magnetization shows scalin typical for the
mean-field Ising model, with the critical exponent $\beta = 1/2$, but other critical
exponents depend on the topology of the underlying complex network.

Primary authors

Andrzej Krawiecki (Faculty of Physics, Warsaw University of Technology) Dr. Tomasz Gradowski (Faculty of Physics, Warsaw University of Technology)

Presentation Materials

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