A Reanalysis of the Hydrodynamic Theory of Fluid, Polar-Ordered Flocks

TL;DR

This paper reanalyzes the hydrodynamic theory of polar-ordered flocks, revealing new linear terms, clarifying the role of nonlinearities in stabilizing long-range order, and discussing implications for scaling in two dimensions.

Contribution

It introduces new linear terms in the hydrodynamic equations and clarifies the effects of equilibrium and nonequilibrium nonlinearities on long-range order.

Findings

New linear terms modify sound mode damping anisotropy.

Equilibrium nonlinearities do not stabilize long-range order in 2D.

Nonequilibrium nonlinearities do stabilize long-range order in 2D.

Abstract

I reanalyze the hydrodynamic theory of fluid, polar ordered flocks. I find new linear terms in the hydrodynamic equations which slightly modify the anisotropy, but not the scaling, of the damping of sound modes. I also find that the nonlinearities allowed {\it in equilibrium} do not stabilize long ranged order in spatial dimensions $d=2$; in accord with the Mermin-Wagner theorem. Nonequilibrium nonlinearities {\it do} stabilize long ranged order in $d=2$, as argued by earlier work. Some of these were missed by earlier work; it is unclear whether or not they change the scaling exponents in $d=2$.