Do two-dimensional dry active nematics keep quasi-long-range order
In plain words
Active nematics are layers of elongated self-driven units that line up without a preferred head or tail. Whether such a layer stays orientationally ordered over large distances, or activity always creates enough defects to destroy the order, is disputed.
Precise statement
In $2\mathrm{D}$ dry active nematics (no momentum conservation, e.g. Chate-Ginelli-Montagne-type particle models), determine whether the ordered phase has quasi-long-range orientational order with algebraically decaying correlations, or whether activity unbinds $+1/2$ and $-1/2$ disclinations at any finite activity so that order is lost beyond a finite length. An answer gives the asymptotic form of the orientational correlation function and the defect density versus system size.
What would settle it
Simulations over several decades of system size measuring orientational correlations and defect density, together with a renormalization-group treatment including defects.