Equilibrium to off-equilibrium crossover in homogeneous active matter

TL;DR

This paper investigates how increasing activity in the Vicsek model causes a crossover from equilibrium to off-equilibrium universality classes, confirmed by simulations showing changes in critical slowing down and a characteristic length scale.

Contribution

It demonstrates the RG-driven crossover between equilibrium and active fixed points in active matter, linking activity levels to dynamical universality class transitions.

Findings

Critical slowing down exponents match RG predictions

A characteristic length scale governs the crossover

Higher activity reduces the active length scale

Abstract

We study the crossover between equilibrium and off-equilibrium dynamical universality classes in the Vicsek model near its ordering transition. Starting from the incompressible hydrodynamic theory of Chen et al \cite{chen2015critical}, we show that increasing the activity leads to a renormalization group (RG) crossover between the equilibrium ferromagnetic fixed point, with dynamical critical exponent $z = 2$, and the off-equilibrium active fixed point, with $z = 1.7$ (in $d=3$). We run simulations of the classic Vicsek model in the near-ordering regime and find that critical slowing down indeed changes with activity, displaying two exponents that are in remarkable agreement with the RG prediction. The equilibrium-to-off-equilibrium crossover is ruled by a characteristic length scale beyond which active dynamics takes over. Such length scale is smaller the larger the activity, suggesting the existence of a general trade-off between activity and system's size in determining the dynamical universality class of active matter.