Criticality and the onset of ordering in the standard Vicsek model

Baglietto, Gabriel; Albano, Ezequiel V.; Candia, Julián

doi:10.1098/rsfs.2012.0021

Cited by 33 publications

(21 citation statements)

References 35 publications

(74 reference statements)

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“…11. This could explain why some studies of the Vicsek model in the small velocity region claim to find a critical transition [33]: as one gets closer and closer to the zero speed limit, the system-size above which one can correctly observe the discontinuous nature of the transition diverges.…”

Section: E Order Parameter and Finite-size Scalingmentioning

confidence: 95%

Flocking with discrete symmetry: The two-dimensional active Ising model

2015

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We study in detail the active Ising model, a stochastic lattice gas where collective motion emerges from the spontaneous breaking of a discrete symmetry. On a two-dimensional lattice, active particles undergo a diffusion biased in one of two possible directions (left and right) and align ferromagnetically their direction of motion, hence yielding a minimal flocking model with discrete rotational symmetry. We show that the transition to collective motion amounts in this model to a bona fide liquid-gas phase transition in the canonical ensemble. The phase diagram in the density-velocity parameter plane has a critical point at zero velocity which belongs to the Ising universality class. In the density-temperature "canonical" ensemble, the usual critical point of the equilibrium liquid-gas transition is sent to infinite density because the different symmetries between liquid and gas phases preclude a supercritical region. We build a continuum theory which reproduces qualitatively the behavior of the microscopic model. In particular, we predict analytically the shapes of the phase diagrams in the vicinity of the critical points, the binodal and spinodal densities at coexistence, and the speeds and shapes of the phase-separated profiles.

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Section: E Order Parameter and Finite-size Scalingmentioning

confidence: 95%

Flocking with discrete symmetry: The two-dimensional active Ising model

2015

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“…The Vicsek model exhibits, at least for not-too-large sizes, a wide regime where correlations peak at the transition and finite-sizescaling holds(Baglietto et al, 2012;Grégoire and Chaté, 2004;Vicsek et al, 1995).…”

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confidence: 99%

Colloquium: Criticality and dynamical scaling in living systems

2018

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A celebrated and controversial hypothesis suggests that some biological systems -parts, aspects, or groups of them-may extract important functional benefits from operating at the edge of instability, halfway between order and disorder, i.e. in the vicinity of the critical point of a phase transition. Criticality has been argued to provide biological systems with an optimal balance between robustness against perturbations and flexibility to adapt to changing conditions, as well as to confer on them optimal computational capabilities, huge dynamical repertoires, unparalleled sensitivity to stimuli, etc. Criticality, with its concomitant scale invariance, can be conjectured to emerge in living systems as the result of adaptive and evolutionary processes that, for reasons to be fully elucidated, select for it as a template upon which further layers of complexity can rest. This hypothesis is very suggestive as it proposes that criticality could constitute a general and common organizing strategy in biology stemming from the physics of phase transitions. However, despite its thrilling implications, this is still in its embryonic state as a well-founded theory and, as such, it has elicited some healthy skepticism. From the experimental side, the advent of high-throughput technologies has created new prospects in the exploration of biological systems, and empirical evidence in favor of criticality has proliferated, with examples ranging from endogenous brain activity and gene-expression patterns, to flocks of birds and insect-colony foraging, to name but a few. Some pieces of evidence are quite remarkable, while in some other cases empirical data are limited, incomplete, or not fully convincing. More stringent experimental set-ups and theoretical analyses are certainly needed to fully clarify the picture. In any case, the time seems ripe for bridging the gap between this theoretical conjecture and its empirical validation. Given the profound implications of shedding light on this issue, we believe that it is both pertinent and timely to review the state of the art and to discuss future strategies and perspectives. Appendix A: Generic Scale invariance 23 Appendix B: Probabilistic models and statistical criticality 24 Appendix C: Adaptation and evolution towards criticality 24 Appendix D: Other putatively critical living systems 25 References 25 arXiv:1712.04499v2 [cond-mat.stat-mech]

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“…On increasing noise there is known to be a transition between the ordered and disordered phase [7]. The nature of this, and similar, transitions has been studied in depth [7][8][9][10][11][12][13][14][15][16] and recent studies have shown that the phase transition of the standard Vicsek model is continuous when the velocity is small [12][13][14]; and it has been argued that large velocities can lead to artefacts related to the boundary conditions [16]. The nature of the transition has also been shown to depend intimately on the type of noise added to the particles [17], which can either be 'angular', where a random angle is added to the orientation of the velocity of a particle, or 'vectorial', in which a random vector is added to the velocity of a particle.…”

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confidence: 99%

Density regulation in strictly metric-free swarms

Pearce

Turner

2014

New J. Phys.

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There is now experimental evidence that nearest-neighbour interactions in flocks of birds are metric free, i.e. they have no characteristic interaction length scale. However, models that involve interactions between neighbours that are assigned topologically are naturally invariant under spatial expansion, supporting a continuous reduction in density towards zero, unless additional cohesive interactions are introduced or the density is artificially controlled, e.g. via a finite system size. We propose a solution that involves a metric-free motional bias on those individuals that are topologically identified to be on an edge of the swarm. This model has only two primary control parameters, one controlling the relative strength of stochastic noise to the degree of co-alignment and another controlling the degree of the motional bias for those on the edge, relative to the tendency to co-align. We find a novel power-law scaling of the real-space density with the number of individuals N as well as a familiar order-to-disorder transition.

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Criticality and the onset of ordering in the standard Vicsek model

Cited by 33 publications

References 35 publications

Flocking with discrete symmetry: The two-dimensional active Ising model

Flocking with discrete symmetry: The two-dimensional active Ising model

Colloquium: Criticality and dynamical scaling in living systems

Density regulation in strictly metric-free swarms

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