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

Nowak, B.; Stoń, Bartosz; Sznajd-Weron, Katarzyna

doi:10.1038/s41598-021-85361-9

Cited by 26 publications

(56 citation statements)

References 55 publications

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“…Several factors may facilitate discontinuous phase transitions, such as: (a) increasing the number of states that the system’s entities (agents, particles, etc.) can take 1 , 16 – 18 , (b) introducing an aversion to change, which can be related to the size of the group needed to influence the agent 19 , 20 or another kind of inertia 3 , 5 , (c) higher dimensionality of the system 21 , higher system degree 5 , or the larger number of layers in the multiplex 22 . Finally, the presence of the annealed instead of the quenched disorder usually promotes discontinuous phase transitions 23 – 26 .…”

Section: Introductionmentioning

confidence: 99%

Discontinuous phase transitions in the q-voter model with generalized anticonformity on random graphs

Abramiuk-Szurlej

Lipiecki

Pawłowski

et al. 2021

Sci Rep

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We study the binary q-voter model with generalized anticonformity on random Erdős–Rényi graphs. In such a model, two types of social responses, conformity and anticonformity, occur with complementary probabilities and the size of the source of influence $$q_c$$ q c in case of conformity is independent from the size of the source of influence $$q_a$$ q a in case of anticonformity. For $$q_c=q_a=q$$ q c = q a = q the model reduces to the original q-voter model with anticonformity. Previously, such a generalized model was studied only on the complete graph, which corresponds to the mean-field approach. It was shown that it can display discontinuous phase transitions for $$q_c \ge q_a + \Delta q$$ q c ≥ q a + Δ q , where $$\Delta q=4$$ Δ q = 4 for $$q_a \le 3$$ q a ≤ 3 and $$\Delta q=3$$ Δ q = 3 for $$q_a>3$$ q a > 3 . In this paper, we pose the question if discontinuous phase transitions survive on random graphs with an average node degree $$\langle k\rangle \le 150$$ ⟨ k ⟩ ≤ 150 observed empirically in social networks. Using the pair approximation, as well as Monte Carlo simulations, we show that discontinuous phase transitions indeed can survive, even for relatively small values of $$\langle k\rangle$$ ⟨ k ⟩ . Moreover, we show that for $$q_a < q_c - 1$$ q a < q c - 1 pair approximation results overlap the Monte Carlo ones. On the other hand, for $$q_a \ge q_c - 1$$ q a ≥ q c - 1 pair approximation gives qualitatively wrong results indicating discontinuous phase transitions neither observed in the simulations nor within the mean-field approach. Finally, we report an intriguing result showing that the difference between the spinodals obtained within the pair approximation and the mean-field approach follows a power law with respect to $$\langle k\rangle$$ ⟨ k ⟩ , as long as the pair approximation indicates correctly the type of the phase transition.

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Section: Introductionmentioning

confidence: 99%

Discontinuous phase transitions in the q-voter model with generalized anticonformity on random graphs

Abramiuk-Szurlej

Lipiecki

Pawłowski

et al. 2021

Sci Rep

Self Cite

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“…On average, the fraction of voters that are always nonconformists is p, whereas the fraction of voters that are always conformists is 1 − p. This approach is considered in Refs. [6,13,15].…”

Section: Annealed and Quenched Modelsmentioning

confidence: 99%

“…We assume that each of the active out-links may connect nodes of the same type τ independently of others with probability P (τ |τ, j; −j), given by one of Eqs. ( 10)- (13). Thus, the number of active out-links that connect nodes of the same type τ , y, is binomially distributed.…”

Section: Pair Approximation For Quenched Modelsmentioning

confidence: 99%

“…In low-dimensional systems, the presence of quenched disorder leads to the elimination of discontinuous phase transitions known as a rounding effect [9][10][11]. In the mean-field regime, on the other hand, discontinuous phase transitions may survive the introduction of quenched disorder [12,13], or they may appear after its introduction [14]. The change of disorder may also not impact the phase transitions at all [15].…”

Section: Introductionmentioning

confidence: 99%

“…The interplay between conformity and nonconformity is used to study social phenomena in many agent-based models [20]. In particular, agents with fixed behavior classified as either conformity or nonconformity can be found in studies on the q-voter model [13,15,21], the majority-vote model [22][23][24], or the Galam model [25]. Quenched disorder may be also related with the interactions between agents [26][27][28][29].…”

Section: Introductionmentioning

confidence: 99%

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Pair approximation for the q-voter models with quenched disorder on networks

Jędrzejewski,

Sznajd-Weron

2021

Preprint

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Using two models of opinion dynamics, the q-voter model with independence and the q-voter model with anticonformity, we discuss how the change of disorder from annealed to quenched affects phase transitions on networks. Up till now, such an analysis has been done only at the mean-field level. To derive phase diagrams on networks, we develop the pair approximation for the quenched versions of the models. This formalism can be also applied to other quenched dynamics of similar kind. The results indicate that such a change of disorder eliminates all discontinuous phase transitions and broadens ordered phases. We show that although the annealed and quenched types of disorder lead to the same result in the q-voter model with anticonformity at the mean-field level, they do lead to distinct phase diagrams on networks. These phase diagrams shift towards each other as the average node degree of a network increases, and eventually, they coincide in the mean-field limit. In contrast, for the q-voter model with independence, the phase diagrams move towards the same direction regardless of the disorder type, and they do not coincide even in the mean-filed limit. To validate our results, we carry out Monte Carlo simulations on random regular graphs and Barabási-Albert networks. Although the pair approximation may incorrectly predict the type of phase transitions for the annealed models, we have not observed such errors for their quenched counterparts.

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Three-State Opinion Q-Voter Model with Bounded Confidence

Radosz

Doniec

2021

Computational Science – ICCS 2021

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

Cited by 26 publications

References 55 publications

Discontinuous phase transitions in the q-voter model with generalized anticonformity on random graphs

Discontinuous phase transitions in the q-voter model with generalized anticonformity on random graphs

Pair approximation for the q-voter models with quenched disorder on networks

Three-State Opinion Q-Voter Model with Bounded Confidence

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