Critical Phenomena in Active Matter

TL;DR

This paper explores how self-propulsion influences phase transitions in active matter by mapping non-equilibrium dynamics to an effective equilibrium framework, revealing the role of noise correlation time on critical behavior.

Contribution

It introduces a mean-field approach using the Unified Colored Noise Approximation to analyze active matter phase transitions, highlighting the impact of noise correlation time on critical points without altering universality classes.

Findings

The critical point shifts with noise correlation time τ.

Universality class remains unchanged despite τ variations.

Good qualitative agreement between theory and simulations at small τ.

Abstract

We investigate the effect of self-propulsion on a mean-field order-disorder transition. Starting from a $\varphi^4$ scalar field theory subject to an exponentially correlated noise, we exploit the Unified Colored Noise Approximation to map the non-equilibrium 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 $\tau$ and the noise strength $D$. Our results suggest that $\tau$ is a crucial ingredient that changes the location of the critical point but, remarkably, not the universality class of the model. 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 wave lengths. 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 a good qualitative agreement at small $\tau$ values.