Power laws of natural swarms are fingerprints of an extended critical region

Abstract

Collective biological systems display power laws for macroscopic quantities and are fertile probing grounds for statistical physics. Besides power laws, natural insect swarms present strong scale-free correlations, suggesting closeness to phase transitions. Swarms exhibit {\em imperfect} dynamic scaling: their dynamical correlation functions collapse into single curves when written as functions of the scaled time $t\xi^{-z}$ ($\xi$: correlation length, $z$: dynamic exponent), but only for short times. Triggered by markers, natural swarms are not invariant under space translations. Measured static and dynamic critical exponents differ from those of equilibrium and many nonequilibrium phase transitions. Here, we show that: (i) the recently discovered scale-free-chaos phase transition of the harmonically confined Vicsek model has a novel extended critical region for $N$ (finite) insects that contains several critical lines. (ii) As alignment noise vanishes, there are power laws connecting critical confinement and noise that allow calculating static critical exponents for fixed $N$. These power laws imply that the unmeasurable confinement strength is proportional to the perception range measured in natural swarms. (iii) Observations of natural swarms occur at different times and under different atmospheric conditions, which we mimic by considering mixtures of data on different critical lines and $N$. Unlike results of other theoretical approaches, our numerical simulations reproduce the previously described features of natural swarms and yield static and dynamic critical exponents that agree with observations.