Anomalous critical and supercritical phenomena in explosive percolation

D’Souza, Raissa M.; Nagler, Jan

doi:10.1038/nphys3378

Cited by 147 publications

(156 citation statements)

References 81 publications

(102 reference statements)

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“…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.…”

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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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confidence: 99%

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

et al. 2017

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“…While subsequent works have shown the Achlioptas process transition was, in fact, a continuous phase transition with unusual finite-size scaling [5][6][7], many related models with alternative mechanisms showing genuinely discontinuous and anomalous transitions have now been discovered (see Ref. [8] and references therein).…”

Section: Introductionmentioning

confidence: 99%

Partial inertia induces additional phase transition in the majority vote model

2017

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Recently it has been aroused a great interest about explosive (i.e., discontinuous) transitions. They manifest in distinct systems, such as synchronization in coupled oscillators, percolation regime, absorbing phase transitions and more recently, in the majority-vote (MV) model with inertia. In the latter, the model rules are slightly modified by the inclusion of a term depending on the local spin (an inertial term). In such case, Chen et al. (Phys Rev. E 95, 042304 (2017)) have found that relevant inertia changes the nature of the phase transition in complex networks, from continuous to discontinuous. Here we give a further step by embedding inertia only in vertices with degree larger than a threshold value k k * , k being the mean system degree and k * the fraction restriction. Our results, from mean-field analysis and extensive numerical simulations, reveal that an explosive transition is presented in both homogeneous and heterogeneous structures for small and intermediate k * 's. Otherwise, large restriction can sustain a discontinuous transition only in the heterogeneous case. This shares some similarity with recent results for the Kuramoto model (Phys Rev. E 91, 022818 (2015)). Surprisingly, intermediate restriction and large inertia are responsible for the emergence of an extra phase, in which the system is partially synchronized and the classification of phase transition depends on the inertia and the lattice topology. In this case, the system exhibits two phase transitions.

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“…Compared with ordinary percolation where the transition is continuous, explosive percolation is marked by an abrupt jump or discontinuous transition to a largescale connectivity through steps that are much smaller than the system size. Though still in its infancy [4], explosive percolation has already attracted enormous interest with some applications, albeit still few, to finite real-world networks. For example, it has been shown that monitoring e-mail: atordesi@unimelb.edu.au the explosive percolation process on modular networks is useful for understanding the underlying community structure of proteins [2] and social networks [3].…”

Section: Introductionmentioning

confidence: 99%

“…Percolation has profound implications for many disordered complex systems in social environments, Nature and technology: e.g., outbreak of an epidemic disease, social upheaval, spread of fire in a forest, computer virus or malware on computer networks, and power grid failure (see [1][2][3][4], and references therein). In multiphase granular and soft matter systems, percolation has been studied extensively in the context of fluid transport and applied in various industrial processes, including oil and gas recovery, dewatering, and in the manufacture of concrete, slurries and pastes [5,6].…”

Section: Introductionmentioning

confidence: 99%

Powder keg divisions in the critical state regime: transition from continuous to explosive percolation

Zhou

Tordesillas

2017

EPJ Web Conf.

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Abstract. The underlying microstructure and dynamics of a dense granular material as it evolves towards the "critical state", a limit state in which the system deforms with an essentially constant volume and stress ratio, remains widely debated in the micromechanics of granular media community. Strain localization, a common mechanism in the large strain regime, further complicates the characterization of this limit state. Here we revisit the evolution to this limit state within the framework of modern percolation theory. Attention is paid to motion transfer: in this context, percolation translates to the emergence of a large-scale connectivity in graphs that embody information on individual grain displacements. We construct each graph G(r) by connecting nodes, representing the grains, within a distance r in the displacement-state-space. As r increases, we observe a percolation transition on G(r). The size of the jump discontinuity increases in the lead up to failure, indicating that the nature of percolation transition changes from continuous to explosive. We attribute this to the emergence of collective motion, which manifests in increasingly isolated communities in G(r). At the limit state, where the jump discontinuity is highest and invariant across the different unjamming cycles (drops in stress ratio), G(r) encapsulates multiple kinematically distinct communities that are mediated by nodes corresponding to those grains in the shear band. This finding casts light on the dual and opposing roles of the shear band: a mechanism that creates powder keg divisions in the sample, while simultaneously acting as a mechanical link that transfers motion through such subdivisions moving in relative rigid-body motion.

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Anomalous critical and supercritical phenomena in explosive percolation

Cited by 147 publications

References 81 publications

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

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

Partial inertia induces additional phase transition in the majority vote model

Powder keg divisions in the critical state regime: transition from continuous to explosive percolation

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