Dynamical Renormalization Group for Mode-Coupling Field Theories with Solenoidal Constraint

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

JOURNAL OF STATISTICAL PHYSICS

SPRINGER

Lugar: Berlin; Año: 2021 vol. 184 p. 26 - 26

0022-4715

The recent inflow of empirical data about the collective behaviour of strongly correlatedbiological systems has brought field theory and the renormalization group into the biophys-ical arena. Experiments on bird flocks and insect swarms show that social forces act on theparticles? velocity through the generator of its rotations, namely the spin, indicating thatmode-coupling field theories are necessary to reproduce the correct dynamical behaviour.Unfortunately, a theory for three coupled fields?density, velocity and spin?has a pro-hibitive degree of intricacy. A simplifying path consists in getting rid of density fluctuationsby studying incompressible systems. This requires imposing a solenoidal constraint on theprimary field, an unsolved problem even for equilibrium mode-coupling theories. Here, weperform an equilibrium dynamic renormalization group analysis of a mode-coupling fieldtheory subject to a solenoidal constraint; using the classification of Halperin and Hohenberg,we can dub this case as a solenoidal Model G. We demonstrate that the constraint produces anew vertex that mixes static and dynamical coupling constants, and that this vertex is essentialto grant the closure of the renormalization group structure and the consistency of dynamicswith statics. Interestingly, although the solenoidal constraint leads to a modification of thestatic universality class, we find that it does not change the dynamical universality class, aresult that seems to represent an exception to the general rule that dynamical universalityclasses are narrower than static ones. Our results constitute a solid stepping stone in the admit-tedly large chasm towards developing an off-equilibrium mode-coupling theory of biologicalgroups.