Equilibrium to off-equilibrium crossover in homogeneous active matter

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.

arXiv comment10 pages, 4 figures

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• Evidence of fluctuation-induced first-order phase transition in active matter
• Mean field theory of chaotic insect swarms
• Dynamical renormalization group for mode-coupling field theories with solenoidal constraint
• Emergent Gauge Symmetry in Active Brownian Matter
• Discrete Laplacian thermostat for flocks and swarms: the fully conserved Inertial Spin Model