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SUMMARY:Phase transitions in the q-voter model with generalized anticonfor
mity
DTSTART;VALUE=DATE-TIME:20201203T171200Z
DTEND;VALUE=DATE-TIME:20201203T171300Z
DTSTAMP;VALUE=DATE-TIME:20230207T214100Z
UID:indico-contribution-376@zakopane.if.uj.edu.pl
DESCRIPTION:Speakers: Jakub Pawłowski (Wroclaw University of Science and
Technology)\, Angelika Abramiuk-Szurlej (Wroclaw University of Science and
Technology)\, Katarzyna Sznajd-Weron (Wroclaw University of Science and T
echnology)\n\nRecent empirical studies provide evidence that so-called soc
ial hysteresis [1] is present in animal [1\, 2\, 3] as well as in human so
cieties [4\, 5\, 6]\, which would suggest that (at least some) phase trans
itions observed in real social systems are discontinuous. It occurs that d
iscontinuous phase transitions are not that typical in models of opinion d
ynamics. Within several versions of the $q$-voter model [7]\, belonging to
the class of the binary-state dynamics [8\, 9]\, only continuous phase tr
ansitions has been observed\, including the original $q$-voter model [10]
or the $q$-voter model with anticonformity [11]. However\, the change of t
ransition from continuous to discontinuous (for $q>5$) has been reported f
or the $q$-voter model with independence [11].\n\nIn [12] we introduce a $
q$-voter model with generalized anticonformity. Previously it was assumed
that the size of the unanimous group of influence needed for both conformi
ty and anticonformity is equal [11]. We abandon this unjustified assumptio
n and introduce a generalized model\, in which the size of the influence g
roup needed for conformity $q_c$ and the size of the group needed for anti
conformity $q_a$ are independent variables and in general $q_c \\neq q_a$.
\n\nWe consider a system of $N$ voters that form vertexes of an arbitrary
network. Each of them is characterized by the dynamical binary variable $S
_i(t) = \\pm 1$\, $i = 1$\, $\\ldots$\, $N$ which\, in case of social syst
ems\, can be interpreted as an opinion on a given subject (yes/no\, agree/
disagree) at a given time $t$. In each elementary time step we randomly ch
oose one agent that will reconsider its opinion. With probability $p$ the
chosen voter behaves like an anticonformist\, whereas with complementary p
robability $1 - p$ like a conformist. In any case we randomly choose a gro
up of influence from the nearest neighbours of the agent without repetitio
ns. The size of the group depends on the voter's response to social pressu
re ($q_a$ for anticonformity\, $q_c$ for conformity). For $q_a = q_c = q$
the model reduces to the original $q$-voter model with anticonformity intr
oduced in [11]. If the group of influence is unanimous\, the voter is infl
uenced by the group and adapts to it (in case of conformity) or rebels aga
inst it (in case of anticonformity).\n\nWe analyse the model on a complete
graph using linear stability analysis\, numerical methods and Landau's th
eory. We calculate the analytical formulas for the lower spinodal and the
tricritical point for which the phase transition changes from continuous t
o discontinuous. It has occurred that the generalized model displays both
continuous and discontinuous phase transitions depending on the sizes of t
he groups of influence needed for conformity $q_c$ and anticonformity $q_a
$. If the parameter $q_c$ is sufficiently larger than $q_a$\, the type of
the phase transition changes to discontinuous.\n\n[1] Doering\, G.N.\, Sch
arf\, I.\, Moeller\, H.V.\, Pruitt\, J.N. *Social tipping points in animal
societies in response to heat stress*. Nature Ecology and Evolution\, 2(8
):1298-1305\, (2018)\n[2] Beekman\, M.\, Sumpter\, D.J.T.\, Ratnieks\, F.L
.W. *Phase transition between disordered and ordered foraging in pharaoh's
ants*. Proceedings of the National Academy of Sciences of the United Stat
es of America\, 98(17):9703-9706\, (2001)\n[3] Pruitt\, J.N.\, Berdahl\, A
.\, Riehl\, C.\, Pinter-Wollman\, N. and Moeller\, H.V.\, Pringle\, E.G.\,
Aplin\, L.M.\, Robinson\, E.J.H.\, Grilli\, J.\, Yeh\, P.\, Savage\, V.M.
\, Price\, M.H.\, Garland\, J.\, Gilby\, I.C.\, Crofoot\, M.C.\, Doering\,
G.N.\, Hobson\, E.A. *Social tipping points in animal societies*. Proceed
ings of the Royal Society B: Biological Sciences\, 285(1887):20181282\, (2
018)\n[4] Clark\, A.E. *Unemployment as a Social Norm: Psychological Evide
nce from Panel Data*. Journal of Labor Economics\, 21(2):323-351\, (2003)\
n[5] Elster\, J. *A Note on Hysteresis in the Social Sciences*. Synthese\,
33(2/4):371-391\, (1976)\n[6] Scheffer\, M.\, Westley\, F.\, Brock\, W. *
Slow response of societies to new problems: Causes and costs*. Ecosystems\
, 6(5):493-502\, (2003)\n[7] Castellano\, C.\, Muñoz\, M.A.\, Pastor-Sato
rras\, R. *Nonlinear q-voter model*. Physical Review E\, 80(4):041129\, (2
009)\n[8] Gleeson\, J.P. *Binary-state dynamics on complex networks: Pair
approximation and beyond*. 3(2):021004\, (2013)\n[9] Jędrzejewski\, A.\,
Sznajd-Weron\, K. *Statistical Physics Of Opinion Formation: is it a SPOOF
?* Comptes Rendus Physique\, 20(4):244-261\, (2019)\n[10] Castellano\, C.\
, Fortunato\, S.\, Loreto\, V. *Statistical physics of social dynamics*. R
eviews of Modern Physics\, 81(2):591-646\, (2009)\n[11] Nyczka\, P.\, Szna
jd-Weron\, K.\, Cisło\, J. *Phase transitions in the q-voter model with t
wo types of stochastic driving*. 86(1):011105\, (2012)\n[12] Abramiuk\, A.
\, Pawłowski\, J.\, Sznajd-Weron\, K. *Is Independence Necessary for a Di
scontinuous Phase Transition within the q-Voter Model?* Entropy\, 21:521\,
(2019)\n\nhttps://zakopane.if.uj.edu.pl/event/16/contributions/376/
RELATED-TO:indico-event-16@zakopane.if.uj.edu.pl
URL:https://zakopane.if.uj.edu.pl/event/16/contributions/376/
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