Scaling Behaviors in Active Model B+ via the Functional Renormalization Group

TL;DR

This paper investigates the scaling behaviors of the active model B+ using the functional renormalization group, revealing fixed points and phase transition mechanisms in nonequilibrium active systems.

Contribution

It derives regulator-independent beta functions for the model, identifies relevant fixed points, and compares FRG results with perturbative methods for active matter.

Findings

Confirmed the existence of a bicritical fixed point.

Identified regions of parameter space with closed RG submodels.

Demonstrated significant differences between FRG and perturbative RG flows.

Abstract

We study the scaling behaviors of the active model B+ using the functional renormalization group (FRG) approach, based on the nonequilibrium effective action formulated via the Martin-Siggia-Rose path-integral formalism. We derive the $\beta$ functions for all couplings of the system in generic $d$ dimensions, revealing regulator independence in various contributions to the renormalization group (RG) flow at specific values for $d$. After identifying specific regions of the parameter space that define submodels closed under RG transformations, we determine all fixed points of potential physical relevance. We confirm the existence of a bicritical fixed point, which was conjectured within the perturbative momentum-shell RG method for being responsible for the transition from bulk phase separation to microphase separation in active systems. We argue that, within the FRG approach, global flows significantly differ from those obtained in its perturbative counterpart.