Partial inertia induces additional phase transition in the majority vote model

Harunari, Pedro E.; Oliveira, Marcelo M. de; Fiore, Carlos E.

doi:10.1103/physreve.96.042305

Cited by 18 publications

(25 citation statements)

References 38 publications

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“…In several cases, a mean field treatment affords a good description of the model properties. By following the main steps from refs 19 , 21 , 24 , 25 , we derive relations for evaluating the order parameter m for fixed f , θ and k [see Methods, Eqs ( 3 – 8 )]. Figure 1 shows the main results for k = 4, 8 and 12.…”

Section: Model and Resultsmentioning

confidence: 99%

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Fundamental ingredients for discontinuous phase transitions in the inertial majority vote model

Encinas¹,

Harunari²,

Oliveira³

et al. 2018

Sci Rep

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Discontinuous transitions have received considerable interest due to the uncovering that many phenomena such as catastrophic changes, epidemic outbreaks and synchronization present a behavior signed by abrupt (macroscopic) changes (instead of smooth ones) as a tuning parameter is changed. However, in different cases there are still scarce microscopic models reproducing such above trademarks. With these ideas in mind, we investigate the key ingredients underpinning the discontinuous transition in one of the simplest systems with up-down Z2 symmetry recently ascertained in [Phys. Rev. E 95, 042304 (2017)]. Such system, in the presence of an extra ingredient-the inertia- has its continuous transition being switched to a discontinuous one in complex networks. We scrutinize the role of three central ingredients: inertia, system degree, and the lattice topology. Our analysis has been carried out for regular lattices and random regular networks with different node degrees (interacting neighborhood) through mean-field theory (MFT) treatment and numerical simulations. Our findings reveal that not only the inertia but also the connectivity constitute essential elements for shifting the phase transition. Astoundingly, they also manifest in low-dimensional regular topologies, exposing a scaling behavior entirely different than those from the complex networks case. Therefore, our findings put on firmer bases the essential issues for the manifestation of discontinuous transitions in such relevant class of systems with Z2 symmetry.

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Section: Model and Resultsmentioning

confidence: 99%

“…By following the formalism from refs 19 , 24 , 25 , the transition rates w −1→1 and w 1→−1 in Eq. ( 4 ) are decomposed as and where denote the probabilities that the node i of degree k , with spin σ i = −1 ( σ i = 1) changes its state according to the majority (minority) rules, respectively.…”

Section: Methodsmentioning

confidence: 99%

Fundamental ingredients for discontinuous phase transitions in the inertial majority vote model

Encinas¹,

Harunari²,

Oliveira³

et al. 2018

Sci Rep

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“…The MV model is also one of the paradigmatic model for studying opinion dynamics, and it has been extensively studied in regular lattices [24][25][26][27][28], random graphs [29,30], and in complex networks including small-world networks [31][32][33], scale-free networks [34][35][36][37], modular networks [38], complete graphs [39], and spatially embedded networks [40]. Some extensions were also proposed, such as multi-state MV models [41][42][43][44][45][46][47], inertial effect [48][49][50], frustration due to anticonformists [51], and cooperation in multilayer structures [52,53].…”

Section: Introductionmentioning

confidence: 99%

Non-Markovian Majority-Vote model

Chen,

Wang,

Shen

et al. 2020

Preprint

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Non-Markovian dynamics pervades human activity and social networks and it induces memory effects and burstiness in a wide range of processes including inter-event time distributions, duration of interactions in temporal networks and human mobility. Here we propose a non-Markovian Majority-Vote model (NMMV) that introduces non-Markovian effects in the standard (Markovian) Majority-Vote model (SMV). The SMV model is one of the simplest two-state stochastic models for studying opinion dynamics, and displays a continuous order-disorder phase transition at a critical noise. In the NMMV model we assume that the probability that an agent changes state is not only dependent on the majority state of his neighbors but it also depends on his age, i.e. how long the agent has been in his current state. The NMMV model has two regimes: the aging regime implies that the probability that an agent changes state is decreasing with his age, while in the anti-aging regime the probability that an agent changes state is increasing with his age. Interestingly, we find that the critical noise at which we observe the order-disorder phase transition is a non-monotonic function of the rate β of the aging (anti-aging) process. In particular the critical noise in the aging regime displays a maximum as a function of β while in the anti-aging regime displays a minimum. This implies that the aging/anti-aging dynamics can retard/anticipate the transition and that there is an optimal rate β for maximally perturbing the value of the critical noise. The analytical results obtained in the framework of the heterogeneous mean-field approach are validated by extensive numerical simulations on a large variety of network topologies.

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“…Originally, it presents a continuous phase transition belonging to distinct universality classes, according to the lattice topology [19][20][21]. More recently [22][23][24], it has been found that the inclusion of inertia in the MV (IMV), e.g. a term proportional to the local spin, can shift the phase transition to a discontinuous phase transition in complex networks [22,23] * fiore@if.usp.br or even in regular lattices [24,25].…”

Section: Introductionmentioning

confidence: 99%

Influence of distinct kinds of temporal disorder in discontinuous phase transitions

Encinas,

Fiore

2020

Preprint

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Based on the MFT arguments, a general description for discontinuous phase transitions in the presence temporal disorder is considered. Our analysis extends the recent findings [Phys. Rev. E 98, 032129 (2018)] by considering other kinds of phase transitions beyond the absorbing ones. The theory is exemplified in the simplest (nonequilibrium) order-disorder (discontinuous) phase transition with "up-down" Z2 symmetry: the inertial majority vote (IMV) model for two kinds of temporal disorder. As for the APT case, the temporal disorder does not suppress the occurrence of discontinuous phase transitions, but remarkable differences emerge when compared with the pure case. A comparison between the distinct kinds of temporal disorder is also performed beyond the MFT for random-regular (RR) complex topologies.

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Partial inertia induces additional phase transition in the majority vote model

Cited by 18 publications

References 38 publications

Fundamental ingredients for discontinuous phase transitions in the inertial majority vote model

Fundamental ingredients for discontinuous phase transitions in the inertial majority vote model

Non-Markovian Majority-Vote model

Influence of distinct kinds of temporal disorder in discontinuous phase transitions

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