Exact scaling exponents of two-dimensional compressible polar flocks · revision history
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Accepted · first revision · record
- Title
- Exact scaling exponents of two-dimensional compressible polar flocks
- Plain
- Flocks of self-propelled particles that align with neighbours can move together in two dimensions, which equilibrium physics forbids for comparable systems. The exact laws governing the fluctuations of such a flock are disputed.
- Precise
- 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.
- Settled by
- 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.
- Kind
- well-posed
- Answer type
- value
- References
- (empty)
- Literature status
- contested
- Status note
- In 2024 Jentsch and Lee (PRL 133, 128301), Ikeda (PRL 133, 258301) and Amoretti et al. (PRE 110, 054108) each proposed exact exponents or a new universality class for the Vicsek ordered phase; these proposals are mutually inconsistent and none is established numerically (2026).
- Posed since
- 1995