Statistical field theory and effective action method for scalar active matter

We employ statistical field theory techniques for coarse graining the steady-state properties of active Ornstein-Uhlenbeck particles. The computation is carried out in the framework of the unified colored noise approximation that allows an effective equilibrium picture. We thus develop a mean-field theory that allows us to describe in a unified framework the phenomenology of scalar active matter. In particular, we are able to describe througha spontaneous symmetry-breaking mechanism two peculiar features of active systems: (i) the accumulation of active particles at the boundaries of a confining container and (ii) motility-induced phase separation (MIPS). We develop a mean-field theory for steric interacting active particles undergoing MIPS and for active Lennard-Jones(ALJ) fluids. Within this framework, we discuss the universality class of MIPS and A LJ fluids, showing that it falls into the Ising universality class. We thus compute analytically the critical lineTc(τ) for both models. In the case of MIPS,Tc(τ) gives rise to a reentrant phase diagram compatible with an inverse transition from liquid togas as the strength of the noise decreases. However, in the case of particles interacting through anisotropic po-tentials, the field theory acquires aφ3term that, in general, cannot be canceled performing the expansion around the critical point. In this case, the Ising critical point might be replaced by a first-order phase-transition region.