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SUMMARY:Discontinous phase transitions in the generalized q-voter model on
random graphs
DTSTART;VALUE=DATE-TIME:20210702T150700Z
DTEND;VALUE=DATE-TIME:20210702T150800Z
DTSTAMP;VALUE=DATE-TIME:20240806T150027Z
UID:indico-contribution-227@indico.fis.agh.edu.pl
DESCRIPTION:Speakers: Jakub Pawłowski (Wrocław University of Science and
Technology)\, Arkadiusz Lipiecki (Wrocław University of Science and Tech
nology)\nWe investigate the binary $q$-voter model with generalized antico
nformity on random Erdős–Rényi graphs. The generalization refers to th
e freedom of choosing the size of the influence group independently for th
e case of conformity $q_c$ and anticonformity $q_a$. This model was studie
d before on the complete graph\, which corresponds to the mean-field appro
ach\, and on such a graph discontinuous phase transitions were observed fo
r $q_c>q_a + \\Delta q$\, where $\\Delta q=4$ for $q_a \\le 3$ and $\\Delt
a q=3$ for $q_a>3$. Examining the model on random graphs allows us to answ
er the question whether a discontinuous phase transition can survive the s
hift to a network with the value of average node degree that is observed i
n real social systems. By approaching the model both within Monte Carlo (M
C) simulations and Pair Approximation (PA)\, we are able to compare the re
sults obtained within both methods and to investigate the validity of PA.
We show that as long as the average node degree of a graph is relatively l
arge\, PA overlaps MC results. On the other hand\, for smaller values of t
he average node degree\, PA gives qualitatively different results than Mon
te Carlo simulations for some values of $q_c$ and $q_a$. In such cases\, t
he phase transition observed in the simulation is continuous on random gra
phs as well as on the complete graph\, whereas PA indicates a discontinuou
s one. We determine the range of model parameters for which PA gives incor
rect results and we present our attempt at validating the assumptions made
within the PA method in order to understand why PA fails\, even on the ra
ndom graph.\n\nhttps://indico.fis.agh.edu.pl/event/69/contributions/227/
LOCATION:ONLINE
URL:https://indico.fis.agh.edu.pl/event/69/contributions/227/
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