Emergent polar order in nonpolar mixtures with nonreciprocal interactions

Self-organization in living and active systems emerges from microscopic interactions, which are governed by symmetries and intrinsic properties of individual constituents. It is possible, however, that spontaneously formed composite units lead to the emergence of large-scale behavior that is completely different from what is expected for the single particles. An example of such occurrences is non-reciprocal active matter, where asymmetric interactions can induce polarity in nonpolar mixtures.

To study this phenomenon, I will present a generic class of active matter models with two scalar fields that represent the concentration of molecular species interacting nonreciprocally. We study the stability of the emergent ordered state, showing the existence of true long-range polar order in two dimensions and above, both at the linear level and by including all relevant nonlinearities in the Renormalization Group sense. We achieve this by uncovering a mapping to the Kardar-Parisi-Zhang universality class for the dynamics of fluctuations. This classification allows us to prove a conclusive violation of the Mermin-Wagner theorem and to predict the large-scale behavior of systems with non-reciprocal interactions at any dimension.

Moreover, natural systems are often three dimensional, leading to momentum conservation in the bulk. To address this scenario, I will extend this dry system to a wet case, incorporating hydrodynamic interactions in a momentum-conserving fluid. The dynamics of the polar order parameter reveal a fluid-mediated linear instability of the ordered state, which is ultimately stabilized by nonlinear effects in the regime of strong non-reciprocity. This result confirms that the emergent non-equilibrium polar pattern is robust also to hydrodynamic couplings.

REFERENCES.
[1] G. Pisegna, S. Saha, R. Golestanian, Emergent polar order in nonpolar mixtures with nonreciprocal interactions, Proceedings of the National Academy of Sciences 121 (51) (2024).
[2] G. Pisegna, N.Rana, R. Golestanian, S. Saha, Non-reciprocal mixtures in suspension: the role of hydrodynamic interactions, Physical Review Letters 135 (10), 108301 (2025).