Hyperuniform Interfaces in Nonequilibrium Phase Coexistence

We show that long-wavelength interfacial fluctuations are strongly suppressed in nonequilibrium phase coexistence between bulk hyperuniform systems. Using simulations of three distinct microscopic models, we demonstrate that hyperuniform interfaces are much smoother than equilibrium ones, with a universal reduction of height fluctuations at large scale. We derive a nonequilibrium interface equation from the field theory of the bulk order parameter, and predict a reduction in height fluctuations, S_{h}(k)≡⟨|h(k)|^{2}⟩∼|k|^{-1}, in stark contrast to equilibrium capillary wave theory where S_{h}(k)∼|k|^{-2}. Our results establish a new universality class for nonequilibrium interfaces, highlighting the fundamental role of suppressed bulk fluctuations in shaping interfacial dynamics far from equilibrium.