Abstract
We employ Statistical Field Theory techniques for coarse-graining the steady-state properties of Active Ornstein-Uhlenbeck particles. The computation is carried on in the framework of the Unified Colored Noise approximation that allows an effective equilibrium picture. We thus develop a mean-field theory that allows to describe in a unified framework the phenomenology of scalar Active Matter. In particular, we are able to describe through spontaneous symmetry breaking mechanism two peculiar features of Active Systems that are (i) The accumulation of active particles at the boundaries of a confining container, and (ii) Motility-Induced Phase Separation (MIPS). \textcolor{black}{We develop a mean-field theory for steric interacting active particles undergoing to MIPS and for Active Lennard-Jones (ALJ) fluids.} \textcolor{black}{Within this framework}, we discuss the universality class of MIPS and ALJ \textcolor{black}{showing that it falls into Ising universality class.} We \textcolor{black}{thus} compute analytically the critical line $T_c(\tau)$ for both models. In the case of MIPS, $T_c(\tau)$ gives rise to a reentrant phase diagram compatible with an inverse transition from liquid to gas as the strength of the noise decreases. \textcolor{black}{However, in the case of particles interacting through anisotropic potentials, } the field theory acquires a $\varphi^3$ term that, \textcolor{black}{in general, cannot be canceled performing the expansion around the critical point.} In this case, the \textcolor{black}{Ising} critical point might \textcolor{black}{be replaced} by a first-order phase transition \textcolor{black}{region}.
Highlights
In nature, there are many diverse examples of living materials [1] ranging from epithelial monolayers [2] to bacterial colonies [3] to dense drops of ants [4]
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 show that some peculiar behaviors of active systems can be captured through an equilibrium statistical field theory approach
Summary
There are many diverse examples of living materials [1] ranging from epithelial monolayers [2] to bacterial colonies [3] to dense drops of ants [4]. Pattern formation in active matter is driven by out-of-equilibrium dynamics and these condensed phases. We present a study on universal properties of a specific class of active matter systems that is described on a large scale by a scalar field theory. Active field theories based on the dynamical evolution of opportune sets of order parameters have been largely employed for capturing the large-scale behavior of active systems [28,29,30,31,32,33,34]. We show that some peculiar behaviors of active systems can be captured through an equilibrium statistical field theory approach
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