Majority-Vote on Directed Small-World Networks

Luz, Edina M. S.; Lima, F. W. S.

doi:10.1142/s0129183107011297

Cited by 39 publications

(40 citation statements)

References 20 publications

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“…Studies on regular lattices showed the critical exponents are the same as those of the Ising model [3][4][5][6][7], in accordance with the conjecture by Grinstein et al [8]. The MV2 model has also been extensively studied in complex networks, including random graphs [9,10], small world networks [11][12][13], scale-free networks [14][15][16], and some others [17,18].…”

Section: Introductionsupporting

confidence: 57%

Discontinuous phase transition in an annealed multi-state majority-vote model

Li¹,

Chen²,

Huang³

et al. 2016

J. Stat. Mech.

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In this paper, we generalize the original majority-vote (MV) model with noise from two states to arbitrary q states, where q is an integer no less than two. The main emphasis is paid to the comparison on the nature of phase transitions between the two-state MV (MV2) model and the three-state MV (MV3) model. By extensive Monte Carlo simulation and mean-field analysis, we find that the MV3 model undergoes a discontinuous order-disorder phase transition, in contrast to a continuous phase transition in the MV2 model. A central feature of such a discontinuous transition is a strong hysteresis behavior as noise intensity goes forward and backward. Within the hysteresis region, the disordered phase and ordered phase are coexisting.

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Section: Introductionsupporting

confidence: 57%

Discontinuous phase transition in an annealed multi-state majority-vote model

Li¹,

Chen²,

Huang³

et al. 2016

J. Stat. Mech.

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show abstract

“…On complex networks, the MVM shows different behavior [16][17][18][19][20][21][22][23]. Campos et al investigated MVM on undirected small-world networks [16] and found the critical exponent ratios γ/ν and β/ν to differ from those of the Ising model [14]; they depend on the rewiring probability.…”

Section: Introductionmentioning

confidence: 99%

“…Campos et al investigated MVM on undirected small-world networks [16] and found the critical exponent ratios γ/ν and β/ν to differ from those of the Ising model [14]; they depend on the rewiring probability. Luz and Lima studied the MVM on a directed small-world network [17] (see Sánchez et al [24] for its construction). Their critical exponent ratios γ/ν and β/ν also are different from those of the Ising model on square lattices and in this case the MVM exponents do not depend on the rewiring probability, in contrast to results of Campos et al [16].…”

Section: Introductionmentioning

confidence: 99%

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Nonequilibrium model on Archimedean lattices

Lima¹

2014

Open Physics

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Abstract:On (4 6 12) and (4 8 2 ) Archimedean lattices, the critical properties of the majority-vote model are considered and studied using the Glauber transition rate proposed by Kwak et al. [Kwak et al., Phys. Rev. E, 75, 061110 (2007)] rather than the traditional majority-vote with noise [Oliveira, J. Stat. Phys. 66, 273 (1992)]. We obtain T and the critical exponents for this Glauber rate from extensive Monte Carlo studies and finite size scaling. The calculated values of the critical temperatures and Binder cumulant are T = 0 651(3) and U * 4 = 0 612(5), and T = 0 667(2) and U * 4 = 0 613(5), for (4 6 12) and (4 8 2 ) lattices respectively, while the exponent (ratios) β/ν, γ/ν and 1/ν are respectively: 0 105(8), 1 48(11) and 1 16(5) for (4 6 12); and 0 113(2), 1 60(4) and 0 84(6) for (4 8 2 ) lattices. The usual Ising model and the majority-vote model on previously studied regular lattices or complex networks differ from our new results. PACS

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“…In the order to achieve his goal he used 44 (LS) Archimedean lattice. However, also with the aim of improve this criterion other researchers studied MVM on several other topologies that are not Archimedeans [39,[43][44][45][46][47][48]. To their surprise all results obtained for the critical exponents are different from results obtained by M. J. Oliveira, and are also different for each topology used.…”

Section: Introductionmentioning

confidence: 99%

Controlling the Tax Evasion Dynamics via Majority-Vote Model on Various Topologies

Lima¹

2012

TEL

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Within the context of agent-based Monte-Carlo simulations, we study the well-known majority-vote model (MVM) with noise applied to tax evasion on simple square lattices (LS), Honisch-Stauffer (SH), directed and undirected Barabasi-Albert (BAD, BAU) networks. In to control the fluctuations for tax evasion in the economics model proposed by Zaklan, MVM is applied in the neighborhood of the noise critical qc to evolve the Zaklan model. The Zaklan model had been studied recently using the equilibrium Ising model. Here we show that the Zaklan model is robust because this can be studied using equilibrium dynamics of Ising model also through the nonequilibrium MVM and on various topologies cited above giving the same behavior regardless of dynamic or topology used here.

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Majority-Vote on Directed Small-World Networks

Cited by 39 publications

References 20 publications

Discontinuous phase transition in an annealed multi-state majority-vote model

Discontinuous phase transition in an annealed multi-state majority-vote model

Nonequilibrium model on Archimedean lattices

Controlling the Tax Evasion Dynamics via Majority-Vote Model on Various Topologies

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