Natural swarms in 3.99 dimensions

The renormalization group is a key set of ideas and quantitative tools of statistical physics that allow for the calculation of universal quantities that encompass the behaviour of different kinds of collective systems. Extension of the predictive power of the renormalization group to collective biological systems would greatly strengthen the effort to put physical biology on a firm basis. Here we present a step in that direction by calculating the dynamical critical exponent z of natural swarms of insects using the renormalization group to order ϵ = 4 − d. We report the emergence of a novel fixed point, 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 ± 0.11) and numerical simulations (1.35 ± 0.04). Our results probe the power of the renormalization group for the quantitative description of collective behaviour, and suggest that universality may also play a decisive role in strongly correlated biological systems.