Diversity of critical phenomena in the ordered phase of polar active fluids

TL;DR

This paper provides a detailed stability analysis of the Toner-Tu model for polar active fluids, revealing new critical points and universality classes in nonequilibrium phase transitions.

Contribution

It identifies four new critical points in the Toner-Tu model and constructs explicit models to realize them, expanding understanding of active matter phase behavior.

Findings

Two fundamental categories of hydrodynamic instabilities identified.

Four new critical points of the Toner-Tu model discovered.

Some critical points exhibit novel nonequilibrium critical behavior.

Abstract

We present a comprehensive analytical linear stability analysis of the Toner-Tu model for polar active fluids in the ordered phase. Our results provide exact instability criteria and demonstrate that all generic hydrodynamic instabilities fall into two fundamental categories, distinguished by their scaling with the wavevector magnitude. By applying a general criticality condition, we show that each instability can give rise to a critical point by fine-tuning only two parameters. We identify four previously unreported critical points of the Toner-Tu model, two of which already display nonequilibrium critical behavior that extends beyond known universality classes at the linear level. We further construct explicit hydrodynamic models that realize each newly identified critical point, establishing their physical attainability and providing concrete targets for future renormalization-group analyses and microscopic model studies. Altogether, our framework offers a unified theoretical foundation and a practical roadmap for the systematic discovery of new universality classes in active matter.