Exact scaling exponents of two-dimensional compressible polar flocks

In the ordered phase of compressible dry polar active matter (Vicsek model, Toner-Tu hydrodynamics) in $d = 2$, determine the roughness exponent $\chi$, anisotropy exponent $\zeta$ and dynamic exponent $z$ of velocity and density fluctuations. The incompressible 2D case is solved exactly by mapping to the 1D KPZ equation (Kardar-Parisi-Zhang, the standard equation for a randomly growing interface; Chen, Lee, Toner 2016). The 1995 conjecture $\chi = -1/5, \zeta = 3/5, z = 6/5$ for the compressible case is inconsistent with large-scale simulations published in 2019. An answer gives exact or controlled values confirmed by simulations that reach the asymptotic regime.

An analytic determination of $\chi$, $\zeta$ and $z$ for $2\mathrm{D}$ compressible flocks, matched by Vicsek-model simulations large enough to rule out crossovers.