Is Independence Necessary for a Discontinuous Phase Transition within the q-Voter Model?

Abramiuk, Angelika; Pawłowski, Jakub; Sznajd-Weron, Katarzyna

doi:10.3390/e21050521

Cited by 27 publications

(32 citation statements)

References 43 publications

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“…Binary opinions are probably the most frequently used microscopic dynamical variables in models of opinion dynamics, such as the linear voter 23 , 44 – 47 and non-linear voter 6 , 13 , 18 , 36 – 40 , 48 – 50 models, or the majority-vote model 7 , 8 , 10 , 11 , 20 , 43 , 51 – 55 . However, it seems that the binary opinion format is not always sufficient and thus the multi-state versions of the voter 23 – 28 , as well as majority-vote model 21 , 22 , 29 – 32 was introduced.…”

Section: Discussionmentioning

confidence: 99%

Discontinuous phase transitions in the multi-state noisy q-voter model: quenched vs. annealed disorder

Nowak

Stoń

Sznajd-Weron

2021

Sci Rep

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We introduce a generalized version of the noisy q-voter model, one of the most popular opinion dynamics models, in which voters can be in one of $$s \ge 2$$ s ≥ 2 states. As in the original binary q-voter model, which corresponds to $$s=2$$ s = 2 , at each update randomly selected voter can conform to its q randomly chosen neighbors only if they are all in the same state. Additionally, a voter can act independently, taking a randomly chosen state, which introduces disorder to the system. We consider two types of disorder: (1) annealed, which means that each voter can act independently with probability p and with complementary probability $$1-p$$ 1 - p conform to others, and (2) quenched, which means that there is a fraction p of all voters, which are permanently independent and the rest of them are conformists. We analyze the model on the complete graph analytically and via Monte Carlo simulations. We show that for the number of states $$s>2$$ s > 2 the model displays discontinuous phase transitions for any $$q>1$$ q > 1 , on contrary to the model with binary opinions, in which discontinuous phase transitions are observed only for $$q>5$$ q > 5 . Moreover, unlike the case of $$s=2$$ s = 2 , for $$s>2$$ s > 2 discontinuous phase transitions survive under the quenched disorder, although they are less sharp than under the annealed one.

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Section: Discussionmentioning

confidence: 99%

Discontinuous phase transitions in the multi-state noisy q-voter model: quenched vs. annealed disorder

Nowak

Stoń

Sznajd-Weron

2021

Sci Rep

Self Cite

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“…Hence, it seems justified to search for such similarities in other related nonequilibrium models. Taking into account that in the noisy q-voter model on random graphs many results in the MFA and PA can be obtained analytically [13][14][15][16][17][18][19], this model, with a sort of AFM interactions included, could be a good candidate for further studies in the abovementioned direction.…”

Section: Discussionmentioning

confidence: 99%

“…It is often investigated by means of nonequilibrium models formed of agents expressing discrete opinions on a given subject, placed in nodes and interacting via edges of a fixed network with topology reflecting the complexity and, possibly, heterogeneity of social contacts [2,3]. Widely studied examples of such models comprise, e.g., the voter model [4][5][6][7][8], the q-voter model called also nonlinear voter model [9][10][11][12], variants of the noisy q-voter model with different forms of stochasticity [13][14][15][16][17][18][19][20][21][22][23], in particular the q-voter model with independence or anticonformism [13][14][15][16]22], the q-neighbor Ising model [24][25][26][27][28] and the majority-vote model [29][30][31][32][33][34][35]. As a rule, in these models, agents can express only one of two possible opinions and thus are represented by two-state spins and interactions between agents have a form of exchange interactions, either explicitly, as in the q-neighbor Ising model, or effectively, in the remaining models.…”

Section: Introductionmentioning

confidence: 99%

Ferromagnetic and spin-glass like transition in the q-neighbor Ising model on random graphs

Krawiecki

2021

Eur. Phys. J. B

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The q-neighbor Ising model is investigated on homogeneous random graphs with a fraction of edges associated randomly with antiferromagnetic exchange integrals and the remaining edges with ferromagnetic ones. It is a nonequilibrium model for the opinion formation in which the agents, represented by two-state spins, change their opinions according to a Metropolis-like algorithm taking into account interactions with only a randomly chosen subset of their q neighbors. Depending on the model parameters in Monte Carlo simulations, phase diagrams are observed with first-order ferromagnetic transition, both first- and second-order ferromagnetic transitions and second-order ferromagnetic and spin-glass-like transitions as the temperature and fraction of antiferromagnetic exchange integrals are varied; in the latter case, the obtained phase diagrams qualitatively resemble those for the dilute spin-glass model. Homogeneous mean-field and pair approximations are extended to take into account the effect of the antiferromagnetic exchange interactions on the ferromagnetic phase transition in the model. For a broad range of parameters, critical temperatures for the first- or second-order ferromagnetic transition predicted by the homogeneous pair approximation show quantitative agreement with those obtained from Monte Carlo simulations; significant differences occur mainly in the vicinity of the tricritical point in which the critical lines for the second-order ferromagnetic and spin-glass-like transitions meet. Graphic abstract

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“…Finally, let us also note that, in general, a typical way (Landau approach) to examine the stability of the solutions is to approximate

with a suitable polynomial (usually of order 4 or 6) and obtain results for critical points. However, it has been shown that even for relatively simple systems [ 30 ] this analysis might not bring the expected outcomes. Moreover, due to high complexity of the problem (high values of

and

) one would need to use high orders of polynomials, making it hard to evaluate in an analytical way.…”

Section: Resultsmentioning

confidence: 99%

A Veritable Zoology of Successive Phase Transitions in the Asymmetric q-Voter Model on Multiplex Networks

Chmiel

Sienkiewicz

Fronczak

et al. 2020

Entropy

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We analyze a nonlinear q-voter model with stochastic noise, interpreted in the social context as independence, on a duplex network. The size of the lobby q (i.e., the pressure group) is a crucial parameter that changes the behavior of the system. The q-voter model has been applied on multiplex networks, and it has been shown that the character of the phase transition depends on the number of levels in the multiplex network as well as on the value of q. The primary aim of this study is to examine phase transition character in the case when on each level of the network the lobby size is different, resulting in two parameters q1 and q2. In a system of a duplex clique (i.e., two fully overlapped complete graphs) we find evidence of successive phase transitions when a continuous phase transition is followed by a discontinuous one or two consecutive discontinuous phase transitions appear, depending on the parameter. When analyzing this system, we even encounter mixed-order (or hybrid) phase transition. The observation of successive phase transitions is a new quantity in binary state opinion formation models and we show that our analytical considerations are fully supported by Monte-Carlo simulations.

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Is Independence Necessary for a Discontinuous Phase Transition within the q-Voter Model?

Cited by 27 publications

References 43 publications

Discontinuous phase transitions in the multi-state noisy q-voter model: quenched vs. annealed disorder

Discontinuous phase transitions in the multi-state noisy q-voter model: quenched vs. annealed disorder

Ferromagnetic and spin-glass like transition in the q-neighbor Ising model on random graphs

A Veritable Zoology of Successive Phase Transitions in the Asymmetric q-Voter Model on Multiplex Networks

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