Equilibrium to off-equilibrium crossover in homogeneous active matter

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*, 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 value of the speed of the particles is the key ingredient to explore the crossover at a numerical level. I am going to focus on the explanation of how it is possible to tune the right microscopic parameter in order to find complete agreement between simulations and predictions of the mesoscopic theory.

*Critical phenomenon of the order-disorder transition in incompressible active fluids. (2015) New Journal of Physics, 17(4), 042002.