Abstract

Experimental data on biological systems of groups of animals show that the validity of scaling laws is one of the fundamental traits of collective behaviour. Strong correlation is indeed the key ingredient to ensure a large-scale coherent motion. Analyzing experimental data on insect swarms, we see how to quantify the degree of correlation in this system and how to reproduce it with theoretical models. Natural swarms show both strong spatial and temporal correlation, expressed by a dynamical critical exponent $z_{exp} = 1.37 \pm 0.11$ linking correlation length and characteristic time scale of the system. Driven by experimental data, we develop a theory able to rationalize this evidence. We use field theoretical techniques and the Renormalization Group (RG) to compute an analytical prediction for the exponent, i.e. $z=1.35$, in very good agreement with experimental results. For the first time, the predictive power of the RG is extended to collective biological systems, strengthening the effort to put physical biology on a firm basis.  Co-Authors: Andrea Cavagna, Luca Di Carlo, Irene Giardina, Tomas S. Grigera,  Stefania Melillo, Leonardo Parisi, Mattia Scandolo.