Quantitative Assessment of the Toner and Tu Theory of Polar Flocks

Abstract

We present a quantitative assessment of the Toner and Tu theory describing the universal scaling of fluctuations in polar phases of dry active matter. Using large scale simulations of the Vicsek model in two and three dimensions, we find the overall phenomenology and generic algebraic scaling predicted by Toner and Tu, but our data on density correlations reveal some qualitative discrepancies. The values of the associated scaling exponents we estimate differ significantly from those conjectured in 1995. In particular, we identify a large crossover scale beyond which flocks are only weakly anisotropic. We discuss the meaning and consequences of these results.

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References in corpus (8)

• Novel type of phase transition in a system of self-driven particles
• Motility-Induced Phase Separation
• Physics of Microswimmers - Single Particle Motion and Collective Behavior
• Collective motion of self-propelled particles interacting without cohesion
• Active matter
• Pattern formation in self-propelled particles with density-dependent motility
• Minimal model for active nematics: quasi-long-range order and giant fluctuations
• Giant fluctuations and structural effects in a flocking epithelium

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