Vortex proliferation in weakly ordered nonreciprocal XY phases

Establish whether the weakly phase-ordered regimes with fluctuation exponent η>1 in the two-dimensional nonreciprocal random-bond XY model are destroyed by vortex proliferation, thereby determining whether only the range 1/2≤η≤1 is physically realizable in that model.

Background

The paper derives a hydrodynamic theory for a two-dimensional nonreciprocal random-bond XY model and an active surface with quenched tangential advection. The theory predicts phase fluctuations of the form ⟨θ²⟩∼[ln(L/a₀)]η, where η is nonuniversal and can exceed one. For the XY realization, θ is compact and therefore supports vortices; for the surface realization, θ is noncompact and vortices are absent.

The authors use heuristic arguments based on the scale-dependent ratio β(ℓ)=κ(ℓ)/D̄(ℓ) and the equilibrium XY vortex-fugacity recursion relation to argue that vortices should remain bounded for η<1 but become unbounded for η>1. They explicitly identify the status of this conclusion as conjectural, noting that its correctness determines whether the η>1 regions can occur in the nonreciprocal XY model or only in the active-surface realization.

References

We conjecture, and support below with heuristic arguments, that vortices in NRB XY models are irrelevant, at least for sufficiently weak noise, when η<1, i.e., in NRB XY models exhibiting stronger order than 2D equilibrium XY models. The same arguments imply that vortices remain relevant, even at arbitrarily weak noise, when (η>1).

— Quenched activity induces nonuniversal scaling in nonreciprocal XY Models and surfaces  (2608.26919 - Mukherjee et al., 27 Aug 2026) in Main text, discussion surrounding Eq. (basic-xy) and Fig. 1 caption