A novel nonequilibrium state of matter: a $d=4-\epsilon$ expansion study of Malthusian flocks

Abstract

We show that "Malthusian flocks" -- i.e., coherently moving collections of self-propelled entities (such as living creatures) which are being "born" and "dying" during their motion -- belong to a new universality class in spatial dimensions $d>2$. We calculate the universal exponents and scaling laws of this new universality class to $O(\epsilon )$ in a $d=4-\epsilon$ expansion, and find these are different from the "canonical" exponents previously conjectured to hold for "immortal" flocks (i.e., those without birth and death) and shown to hold for incompressible flocks with spatial dimensions in the range of $2<d\le 4$. We also obtain a universal amplitude ratio relating the damping of transverse and longitudinal velocity and density fluctuations in these systems. Furthermore, we find a universal separatrix in real ($\mathbf{r}$) space between two regions in which the equal time density correlation $⟨\delta \rho (\mathbf{r},t)\delta \rho (0,t)⟩$ has opposite signs. Our expansion should be quite accurate in $d=3$, allowing precise quantitative comparisons between our theory, simulations, and experiments.

48 pages, 7 figures. This is the long paper accompanying the short paper "Moving, reproducing, and dying beyond Flatland: Malthusian flocks in dimensions $d>2$" [arXiv:2001.01300]

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• Quantitative Assessment of the Toner and Tu Theory of Polar Flocks
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Cited by in corpus (12)

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• Moving, reproducing, and dying beyond Flatland: Malthusian flocks in dimensions $d>2$
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• Packed swarms on dirt: two-dimensional incompressible flocks with quenched and annealed disorder
• Hohenberg-Mermin-Wagner type theorems for equilibrium models of flocking
• Evidence of fluctuation-induced first-order phase transition in active matter
• A new universality class describes Vicsek's flocking phase in physical dimensions
• Novel critical phenomena in compressible polar active fluids: Dynamical and Functional Renormalization Group Studies
• Don't look back: Ordering and defect cloaking in non-reciprocal lattice XY models
• Thermodynamic constraints and exact scaling exponents of flocking matter
• An Infinite Set of Integral Formulae for Polar, Nematic, and Higher Order Structures at the Interface of Motility-Induced Phase Separation
• Dynamics of packed swarms: time-displaced correlators of two dimensional incompressible flocks