Statistical field theory and effective action method for scalar active matter

Abstract

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 through a 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 ALJ fluids, showing that it falls into the Ising universality class. We thus compute analytically the critical line T_{c}(τ) for both models. In the case of MIPS, T_{c}(τ) gives rise to a reentrant phase diagram compatible with an inverse transition from liquid to gas as the strength of the noise decreases. However, in the case of particles interacting through anisotropic potentials, the field theory acquires a φ^{3} term 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.