Critical phenomenon of the order-disorder transition in incompressible active fluids

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.