Emergent polar order in non-polar mixtures with non-reciprocal interactions

TL;DR

This paper demonstrates the emergence of true long-range polar order in non-reciprocal active matter mixtures in two dimensions, challenging the Mermin-Wagner theorem through a mapping to established universality classes.

Contribution

It introduces a novel scalar active matter model with non-reciprocal interactions that exhibits stable long-range polar order, supported by a mapping to the Toner-Tu and KPZ universality classes.

Findings

Long-range polar order exists in 2D non-reciprocal mixtures.

The effective field theory belongs to the KPZ universality class.

The results violate the Mermin-Wagner theorem in this context.

Abstract

Phenomenological rules that govern the collective behaviour of complex physical systems are powerful tools because they can make concrete predictions about their universality class based on generic considerations, such as symmetries, conservation laws, and dimensionality. While in most cases such considerations are manifestly ingrained in the constituents, novel phenomenology can emerge when composite units associated with emergent symmetries dominate the behaviour of the system. We study a generic class of active matter systems with non-reciprocal interactions and demonstrate 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 of our scalar active mixture theory to the Toner-Tu theory of dry polar active matter by employing a suitably defined polar order parameter. We then demonstrate that the complete effective field theory -- which includes all the soft modes and the relevant nonlinear terms -- belongs to the (Burgers-) Kardar-Parisi-Zhang universality class. This classification allows us to prove the stability of the emergent polar long-range order in scalar non-reciprocal mixtures in two dimensions, and hence a conclusive violation of the Mermin-Wagner theorem.