Isotropic majority-vote model on a square lattice

Oliveira, Mário J. de

doi:10.1007/bf01060069

Cited by 282 publications

(401 citation statements)

References 16 publications

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“…In these cases the measurableα loc roughness exponent is different fromα and may satisfy different scaling law (Brú and al., 1998;Dasgupta et al, 1996;H. Yang and Lu, 1994;Jeffries et al, 1996;Krug, 1997;Rodríguez, 1996, 1997;López and Schmittbuhl, 1998;Morel and al., 1998;Oliveira, 1992;Schroeder and al., 1993). Surfaces in d + 1 dimensional systems can be mapped onto a time step of a d dimensional particle reactiondiffusion or spin models.…”

Section: Interface Growth Classesmentioning

confidence: 99%

Universality classes in nonequilibrium lattice systems

2004

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This work is designed to overview our present knowledge about universality classes occurring in nonequilibrium systems defined on regular lattices. In the first section I summarize the most important critical exponents, relations and the field theoretical formalism used in the text. In the second section I briefly address the question of scaling behavior at first order phase transitions. In section three I review dynamical extensions of basic static classes, show the effect of mixing dynamics and the percolation behavior. The main body of this work is given in section four where genuine, dynamical universality classes specific to nonequilibrium systems are introduced. In section five I continue overviewing such nonequilibrium classes but in coupled, multi-component systems. Most of the known nonequilibrium transition classes are explored in low dimensions between active and absorbing states of reaction-diffusion type of systems. However by mapping they can be related to universal behavior of interface growth models, which I overview in section six. Finally in section seven I summarize families of absorbing state system classes, mean-field classes and give an outlook for further directions of research.

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Section: Interface Growth Classesmentioning

confidence: 99%

Universality classes in nonequilibrium lattice systems

2004

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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].…”

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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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“…Where a is close to n/2, then there will be similarities between these transmission dynamics and majority vote models (e.g. [11,12]) although behaviour cessation will be qualitatively different.…”

Section: Dynamical Parametersmentioning

confidence: 99%

“…Modelling techniques have so far typically involved either explicit stochastic simulation [3 -6], or else application of mathematical models originally developed for other applications, such as the Susceptible-Infectious-Susceptible (SIS) epidemic model considered by Kiss et al [7] and Funk et al [8]. An alternative is to use a discrete-time formalism [9,10], next-generation arguments [5] or methods from statistical physics [11,12] to obtain results about asymptotic behaviour of socially motivated models, although typically calculating transient features of system dynamics requires Monte Carlo simulation.…”

Section: Introductionmentioning

confidence: 99%

Modelling behavioural contagion

House

2011

J. R. Soc. Interface.

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The last decade has seen much work on quantitative understanding of human behaviour, with online social interaction offering the possibility of more precise measurement of behavioural phenomena than was previously possible. A parsimonious model is proposed that incorporates several observed features of behavioural contagion not seen in existing epidemic model schemes, leading to metastable behavioural dynamics.

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Isotropic majority-vote model on a square lattice

Cited by 282 publications

References 16 publications

Universality classes in nonequilibrium lattice systems

Universality classes in nonequilibrium lattice systems

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

Modelling behavioural contagion

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