Critical phenomena in active matter

We investigate the effect of self-propulsion on a mean-field order-disorder transition. Starting from a φ^{4} scalar field theory subject to an exponentially correlated noise, we exploit the unified colored-noise approximation to map the nonequilibrium active dynamics onto an effective equilibrium one. This allows us to follow the evolution of the second-order critical point as a function of the noise parameters: the correlation time τ and the noise strength D. Our results suggest that the universality class of the model remains unchanged. We also estimate the effect of Gaussian fluctuations on the mean-field approximation finding an Ornstein-Zernike-like expression for the static structure factor at long wavelengths. Finally, to assess the validity of our predictions, we compare the mean-field theoretical results with numerical simulations of active Lennard-Jones particles in two and three dimensions, finding good qualitative agreement at small τ values.