Nonmutual torques and the unimportance of motility for long-range order in two-dimensional flocks

TL;DR

This paper investigates how asymmetric torques in two-dimensional flocks lead to buckling instabilities and affect information propagation, emphasizing the role of nonreciprocal interactions and motility in flock order.

Contribution

It introduces a model with asymmetric interparticle torques and spin angular momentum, revealing their impact on flock stability and information dynamics.

Findings

Asymmetric torques cause buckling instability in flocks.

Nonreciprocal interactions enable non-zero advection speed of polarization.

Absence of detailed balance is key to the observed phenomena.

Abstract

As the constituent particles of a flock are polar and in a driven state, their interactions must, in general, be fore-aft asymmetric and non-reciprocal. Within a model that explicitly retains the classical spin angular momentum field of the particles we show that the resulting asymmetric contribution to interparticle torques, if large enough, leads to a buckling instability of the flock. Precisely this asymmetry also yields a natural mechanism for a difference between the speed of advection of information along the flock and the speed of the flock itself, concretely establishing that the absence of detailed balance, and not merely the breaking of Galilean invariance, is crucial for this distinction. To highlight this we construct a model of asymmetrically interacting spins fixed to lattice points and demonstrate that the speed of advection of polarisation remains non-zero. We delineate the conditions on parameters and wavenumber for the existence of the buckling instability. Our theory should be consequential for interpreting the behaviour of real animal groups as well as experimental studies of artificial flocks composed of polar motile rods on substrates.