Dynamical Renormalization Group Approach to the Collective Behavior of Swarms

CAVAGNA, ANDREA; GRANDINETTI, LUCA; DI CARLO, LUCA; GRIGERA, TOMAS S.; GIARDINA, IRENE; PISEGNA, GIULIA

PHYSICAL REVIEW LETTERS

AMER PHYSICAL SOC

Año: 2019 vol. 123

0031-9007

We study the critical behavior of a model with nondissipative couplings aimed at describing thecollective behavior of natural swarms, using the dynamical renormalization group under a fixed-networkapproximation. At one loop, we find a crossover between an unstable fixed point, characterized by adynamical critical exponent z 1⁄4 d=2, and a stable fixed point with z 1⁄4 2, a result we confirm throughnumerical simulations. The crossover is regulated by a length scale given by the ratio between the transportcoefficient and the effective friction, so that in finite-size biological systems with low dissipation, dynamicsis ruled by the unstable fixed point. In three dimensions this mechanism gives z 1⁄4 3=2, a value significantlycloser to the experimental window, 1.0 ≤ z ≤ 1.3, than the value z ≈ 2 numerically found in fullydissipative models, either at or off equilibrium. This result indicates that nondissipative dynamicalcouplings are necessary to develop a theory of natural swarms fully consistent with experiments.