Universality in Incompressible Active Fluid: Effect of Non-local Shear Stress
Phase transitions in active fluids attracted significant attention within the last decades. Recent results show [L. Chen et al., New J. Phys. 17, 042002 (2015)] that an order-disorder phase transition in incompressible active fluids belongs to a new universality class. In this work, we further investigate this type of phase transition and focus on the effect of long-range interactions. This is achieved by introducing a non-local shear stress into the hydrodynamic description, which leads to superdiffusion of the velocity field, and can be viewed as a result of the active particles performing Levy walks. The universal properties in the critical region are derived by performing a perturbative renormalization group analysis of the corresponding response functional within the one-loop approximation. We show that the effect of non-local shear stress decreases the upper critical dimension of the model, and can lead to the irrelevance of the active fluid self-advection with the resulting model belonging to an unusual 'long-range Model A' universality class not reported before. Moreover, when the degree of non-locality is sufficiently high all non-linearities become irrelevant and the mean-field description is valid in any spatial dimension.