Natural Swarms in $\bf 3.99$ 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 ($1.35 \pm 0.04$).