Natural Swarms in $\bf 3.99$ Dimensions

TL;DR

This paper uses renormalization group analysis to calculate the critical dynamical exponent of insect swarms in nearly four dimensions, revealing a new fixed point that aligns with experimental and simulation results in three dimensions.

Contribution

It introduces a novel fixed point in the theoretical model of swarms where activity and inertia are both relevant, advancing understanding of swarm dynamics.

Findings

Critical exponent in 3D is 1.35, matching experiments.

A new fixed point emerges with both activity and inertia relevant.

The analysis extends to 3.99 dimensions using epsilon expansion.

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 ($1.35 \pm 0.04$).