Nonequilibrium Ising model with competing dynamics: A MFRG approach

Marques, Marta

doi:10.1016/0375-9601(90)90954-m

Cited by 26 publications

(20 citation statements)

References 7 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: 62%

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: 62%

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

Lima¹

2012

TEL

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“…This conjecture was found in several models that do not obey detailed balance [2,3,4]. Campos et al [5] investigated the majority-vote model on small-world network by rewiring the two dimensional square lattice.…”

Section: Introductionmentioning

confidence: 94%

Majority-Vote on Directed Barabási–albert Networks

Lima

2006

Int. J. Mod. Phys. C

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On directed Barabási-Albert networks with two and seven neighbours selected by each added site, the Ising model was seen not to show a spontaneous magnetisation. Instead, the decay time for flipping of the magnetisation followed an Arrhenius law for Metropolis and Glauber algorithms, but for Wolff cluster flipping the magnetisation decayed exponentially with time. On these networks the Majority-vote model with noise is now studied through Monte Carlo simulations. However, in this model, the order-disorder 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 connectivity z of the directed Barabási-Albert network. The critical exponentes β/ν, γ/ν and 1/ν were calculated for several values of z.Keywords:Monte Carlo simulation,vote , networks, nonequilibrium. IntroductionIt 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 [1]. This conjecture was found in several models that do not obey detailed balance [2,3,4]. Campos et al.[5] investigated the majority-vote model on small-world network by rewiring the two dimensional square lattice. These small-world networks, aside from presenting quenched disorder, also posses long-range interactions. They found that the critical exponents γ/ν and β/ν are different from the Ising model and depend on the rewiring probability. However, it was not evident that the exponent change was due to the disordered nature of the network or due to the presence of long-range interactions. Lima et al.[6] studied the majority-vote model on Voronoi-Delaunay random lattices with periodic boundary conditions. These lattices posses natural quenched disorder in their conecctions. They showed that presence of quenched connectivity disorder is enough to alter the exponents β/ν and γ/ν from the pure model and therefore that is a relevant term to such non-equilibrium phase-transition. Sumour and Shabat [7,8]

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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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Nonequilibrium Ising model with competing dynamics: A MFRG approach

Cited by 26 publications

References 7 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 Barabási–albert Networks

Majority-Vote on Directed Small-World Networks

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