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 ($1.35\pm 0.04$).

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

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