Natural Swarms in $3.99$ Dimensions

Abstract

The dynamical critical exponent $z$ of natural swarms of insects is calculated using the renormalization group to order $\epsilon =4-d$. A novel fixed point emerges, where both activity and inertia are relevant. In three dimensions the critical exponent at the new fixed point is $z=1.35$, in agreement with both experiments ($1.37\pm 0.11$) and numerical simulations ($1.35\pm 0.04$).

Numerical simulations to validate RG predictions added. Experimental assesment of the dynamic critical exponent revised. 72 pages, 24 figures, 1 table

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• Mean field theory of chaotic insect swarms
• Field theories and quantum methods for stochastic reaction-diffusion systems
• Discrete Laplacian Thermostat for Spin Systems with Conserved Dynamics
• Scale-free chaos in the 2D harmonically confined Vicsek model
• Power laws of natural swarms are fingerprints of an extended critical region
• Hermitian and non-Hermitian topology in active matter
• Discrete Laplacian thermostat for flocks and swarms: the fully conserved Inertial Spin Model
• The Inertial Spin Model of flocking with position-dependent forces