Critical phenomenon of the order–disorder transition in incompressible active fluids - Leiming Chen; John Toner; Chiu Fan Lee (New Journal of Physics, 2015)
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 $\mathcal{O}(ε )$ in an $ε =4-d$ 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.