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 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 ${\phi }^3$ 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}.

References in corpus (24)

• Interaction Ruling Animal Collective Behaviour Depends on Topological rather than Metric Distance: Evidence from a Field Study
• Motility-Induced Phase Separation
• Statistical Mechanics of Interacting Run-and-Tumble Bacteria
• Topology and Dynamics of Active Nematic Vesicles
• When are active Brownian particles and run-and-tumble particles equivalent? Consequences for motility-induced phase separation
• Diffusive transport without detailed balance in motile bacteria: Does microbiology need statistical physics?
• Pressure and Phase Equilibria in Interacting Active Brownian Spheres
• A self-propelled particle in an external potential: is there an effective temperature?
• Effective Interactions in Active Brownian Suspensions
• Multidimensional Stationary Probability Distribution for Interacting Active Particles
• Generalized energy equipartition in harmonic oscillators driven by active baths
• Emergent oscillations assist obstacle negotiation during ant cooperative transport
• Active colloidal suspensions: Clustering and phase behavior
• Fluctuations and Rheology in Active Bacterial Suspensions
• Glassy dynamics of athermal self-propelled particles: Computer simulations and a nonequilibrium microscopic theory
• Directed transport of active particles over asymmetric energy barriers
• A self-driven phase transition drives Myxococcus xanthus fruiting body formation
• Filling an emulsion drop with motile bacteria
• Stationary superstatistics distributions of trapped run-and-tumble particles
• Phase coexistence of active Brownian particles
• From bulk to microphase separation in scalar active matter: A perturbative renormalization group analysis
• Stable Solution of the Simplest Spin Model for Inverse Freezing
• Active hard-spheres in infinitely many dimensions
• Effective equilibrium picture in $xy-$model with exponentially correlated noise

Cited by in corpus (10)

• Universality class of the motility-induced critical point in large scale off-lattice simulations of active particles
• Critical active dynamics is captured by a colored-noise driven field theory
• Critical behavior of active Brownian particles: Connection to field theories
• Microscopic field theory for structure formation in systems of self-propelled particles with generic torques
• The most probable path of Active Ornstein-Uhlenbeck particles
• Site-percolation transition of run-and-tumble particles
• Irreversibility in Non-reciprocal Chaotic Systems
• Universality of the complete-graph Potts model with $0<q\le 2$
• Phase separation of self-propelled disks with ferromagnetic and nematic alignment
• How non-equilibrium correlations in active matter reveal the topological crossover in glasses