Majority-vote model on spatially embedded networks: Crossover from mean-field to Ising universality classes

We study the contact process on spatially embedded networks, consisting of a regular square lattice with long-range connections. To generate the networks, a long-range connection is randomly added to each node i of a square lattice, following the probability, Pij ∼ r −α ij , where rij is the Manhattan distance between nodes i and j, and the exponent α is a tunable parameter. Extensive Monte Carlo simulations and a finite-size scaling analysis for different values of α reveal a crossover from the mean-field to 2d Directed Percolation universality class with increasing α, in the range 3 < α < 4.

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“…In Ref. [26] the authors show also that the Binder cumulant at the critical parameter is α-dependent.…”

Section: Resultsmentioning

confidence: 96%

Crossover from mean-field to 2d Directed Percolation in the contact process

Santos¹,

Filho²,

Araújo³

et al. 2018

Physica A: Statistical Mechanics and its Applications

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“…The BVM does not satisfy the condition of detailed balance, and therefore the zeroth law of thermodynamics is not satisfied. This feature is shared with other studied irreversible models [16][17][18][19][20][21][22][23][24][25]. The parameter N P CS defines the range of interactions and we consider the scenario of medium-range interactions [15,26].…”

Section: Introductionmentioning

confidence: 91%

Noise induced phase transition in the S-state block voter model

Araújo

Filho

Moreira

2018

Physica A: Statistical Mechanics and its Applications

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We use Monte Carlo simulations and finite-size scaling theory to investigate the phase transition and critical behavior of the S-state block voter model on square lattices. It is shown that the system exhibits an order-disorder phase transition at a given value of the noise parameter, which changes from a continuous transition for S ≤ 4 to a discontinuous transition for S ≥ 5. Moreover, for the cases of continuous transition, the calculated critical exponents indicate that the present studied nonequilibrium model system is in the same universality class of its counterpart equilibrium twodimensional S-state Potts model. We also provide a first estimation of the long-range exponents governing the dependence on the range of interaction of the magnetization, the susceptibility, and the derivative of Binder's cumulant.

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“…It was later generalized to a cubic lattice [27], small-world networks [28,29], random graphs [30,31], scale-free networks [32,33], and spatially embedded networks [34]. The impact of site dilution and agent diffusion on the critical behavior of the majority-vote model has also been addressed recently [35,36], as well as the presence of two types of noises [37].…”

Section: Introductionmentioning

confidence: 99%

Majority-vote model with limited visibility: an investigation into filter bubbles

Vilela,

Pereira,

Dias

et al. 2020

Preprint

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The dynamics of opinion formation in a society is a complex phenomenon where many variables play an important role. Recently, the influence of algorithms to filter which content is fed to social networks users has come under scrutiny. Supposedly, the algorithms promote marketing strategies, but can also facilitate the formation of filters bubbles in which a user is most likely exposed to opinions that conform to their own. In the two-state majority-vote model an individual adopts an opinion contrary to the majority of its neighbors with probability q, defined as the noise parameter.Here, we introduce a visibility parameter V in the dynamics of the majority-vote model, which equals the probability of an individual ignoring the opinion of each one of its neighbors. For V = 0.5 each individual will, on average, ignore the opinion of half of its neighboring nodes. We employ Monte Carlo simulations to calculate the critical noise parameter as a function of the visibility q c (V ) and obtain the phase diagram of the model. We find that the critical noise is an increasing function of the visibility parameter, such that a lower value of V favors dissensus. Via finite-size scaling analysis we obtain the critical exponents of the model, which are visibility-independent, and show that the model belongs to the Ising universality class. We compare our results to the case of a network submitted to a static site dilution, and find that the limited visibility model is a more subtle way of inducing opinion polarization in a social network.

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Majority-vote model on spatially embedded networks: Crossover from mean-field to Ising universality classes

Cited by 12 publications

References 47 publications

Crossover from mean-field to 2d Directed Percolation in the contact process

Crossover from mean-field to 2d Directed Percolation in the contact process

Noise induced phase transition in the S-state block voter model

Majority-vote model with limited visibility: an investigation into filter bubbles

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