MAJORITY-VOTE MODEL ON (3, 4, 6, 4) AND (3<sup>4</sup>, 6) ARCHIMEDEAN LATTICES

Lima, F. W. S.; Malarz, Krzysztof

doi:10.1142/s0129183106009849

Cited by 47 publications

(50 citation statements)

References 23 publications

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“…This conjecture was confirmed for various Archimedean lattices and in several models that do not obey detailed balance [19][20][21][22]. The majority-vote model (MVM) is a nonequilibrium model proposed by M. J. Oliveira in 1992 [20] and defined by stochastic dynamics with local rules and with up-down symmetry on a regular lattice shows a second-order phase transition with critical exponents β, γ, and ν which characterize the system in the vicinity of the phase transition identical with those of the equilibrim Ising model [1] for regular lattices.…”

Section: Introductionmentioning

confidence: 63%

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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Section: Introductionmentioning

confidence: 63%

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

Lima¹

2012

TEL

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“…It has been argued that nonequilibrium stochastic spin systems on regular square lattice with up-down symmetry fall in the universality class of the equilibrium Ising model [9]. This conjecture was found in several models that do not obey detailed balance [10,11,12,13,14]. Lima [15,16] investigated the majority-vote model on directed and undirected Barabási-Albert network and calculated the β/ν, γ/ν, and 1/ν exponents and these are different from the Ising model and depend on the values of connectivity z of the Barabási-Albert network.…”

Section: Introductionmentioning

confidence: 99%

Majority-Vote on Directed Small-World Networks

Luz

Lima

2007

Int. J. Mod. Phys. C

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On directed Small-World networks the Majority-vote model with noise is now studied through Monte Carlo simulations. In this model, the orderdisorder phase transition of the order parameter is well defined in this system. We calculate the value of the critical noise parameter q c for several values of rewiring probability p of the directed Small-World network. The critical exponentes β/ν, γ/ν and 1/ν were calculated for several values of p.

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“…The MV model is one of the simplest nonequilibrium generalizations of the Ising model that displays a continuous order-disorder phase transition at a critical value of noise [28]. It has been extensively studied in the context of complex networks, including random graphs [29,30], small world networks [31][32][33], and scale-free networks [34,35]. However, the continuous nature of the order-disorder phase transition is not affected by the topology of the underlying networks [36].…”

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confidence: 99%

First-order phase transition in a majority-vote model with inertia

et al. 2017

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We generalize the original majority-vote model by incorporating an inertia into the microscopic dynamics of the spin flipping, where the spin-flip probability of any individual depends not only on the states of its neighbors, but also on its own state. Surprisingly, the order-disorder phase transition is changed from a usual continuous type to a discontinuous or an explosive one when the inertia is above an appropriate level. A central feature of such an explosive transition is a strong hysteresis behavior as noise intensity goes forward and backward. Within the hysteresis region, a disordered phase and two symmetric ordered phases are coexisting and transition rates between these phases are numerically calculated by a rare-event sampling method. A mean-field theory is developed to analytically reveal the property of this phase transition. Recently, explosive or discontinuous transitions in complex networks have received growing attention since the discovery of an abrupt percolation transition in random networks [8,9] and scale-free networks [10,11]. Later studies affirmed that this transition is actually continuous but with an unusual finite size scaling [12][13][14], yet many related models show truly discontinuous and anomalous transitions (cf.[15] for a recent review). Striking different from continuous phase transitions, in an explosive transition an infinitesimal increase of the control parameter can give rise to a considerable macroscopic effect. Subsequently, an explosive phenomenon was found in the dynamics of cascading failures in interdependent networks [16][17][18], in contrast to the secondorder continuous phase transition found in isolated networks. More recently, such explosive phase transitions have been reported in various systems, such as explosive synchronization due to a positive correlation between the degrees of nodes and the natural frequencies of the oscillators [19][20][21] [25][26][27].In this paper we report an explosive order-disorder phase transition in a generalized majority-vote (MV) model by incorporating the effect of individuals' inertia (called inertial MV model ). The MV model is one of the simplest nonequilibrium generalizations of the Ising model that displays a continuous order-disorder phase transition at a critical value of noise [28]. It has been extensively studied in the context of complex networks, including random graphs [29,30], small world networks [31][32][33], and scale-free networks [34,35]. However, the continuous nature of the order-disorder phase transition is not affected by the topology of the underlying networks [36]. In our model, we have included a substantial change to make it more realistic, namely the state update of each node depends not only on the states of its neighboring nodes, but also on its own state. In fact, in a social or biological context individuals have a tendency for beliefs to endure once formed. In a recent experimental study, behavioral inertia was found to be essential for collective turning of starling flocks [37]. We refer this m...

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MAJORITY-VOTE MODEL ON (3, 4, 6, 4) AND (3⁴, 6) ARCHIMEDEAN LATTICES

Cited by 47 publications

References 23 publications

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

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

Majority-Vote on Directed Small-World Networks

First-order phase transition in a majority-vote model with inertia

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MAJORITY-VOTE MODEL ON (3, 4, 6, 4) AND (34, 6) ARCHIMEDEAN LATTICES

Cited by 47 publications

References 23 publications

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

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

Majority-Vote on Directed Small-World Networks

First-order phase transition in a majority-vote model with inertia

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MAJORITY-VOTE MODEL ON (3, 4, 6, 4) AND (3⁴, 6) ARCHIMEDEAN LATTICES