Critical Phenomenon of the Order-Disorder Transition in Incompressible Flocks

TL;DR

This paper investigates the phase transition in incompressible active particle systems, revealing a continuous transition belonging to a new universality class, with critical exponents derived analytically.

Contribution

It provides the first analytical study of a phase transition in an incompressible active matter system, identifying a new universality class.

Findings

Transition is continuous in incompressible systems

Critical exponents calculated to first order in epsilon expansion

Derived two exact scaling relations

Abstract

We study incompressible systems of motile particles with alignment interactions. Unlike their compressible counterparts, in which the order-disorder (i.e., moving to static) transition, tuned by either noise or number density, is discontinuous, in incompressible systems this transition can be continuous, and belongs to a new universality class. We calculate the critical exponents to $O(\epsilon)$in an $\epsilon=4-d$ expansion, and derive two exact scaling relations. This is the first analytic treatment of a phase transition in a new universality class in an active system.