Critical active dynamics is captured by a colored-noise driven field theory

• Published in: Communications physics Vol. 5; no. 1; pp. 1 - 10
• Main Authors: Maggi, Claudio, Gnan, Nicoletta, Paoluzzi, Matteo, Zaccarelli, Emanuela, Crisanti, Andrea
• Format: Journal Article
• Language: English
• Published: London Nature Publishing Group UK 14-03-2022; Nature Publishing Group; Nature Portfolio
• Subjects: 639/766/119/2795; 639/766/530/2795; Critical point; Equilibrium; Field theory; Ising model; Noise; Physics; Physics and Astronomy
• ISSN: 2399-3650; 2399-3650
• DOI: 10.1038/s42005-022-00830-5

Active matter may sometimes behave almost indistinguishably from equilibrium matter. This is particularly evident for some particle-based models and active field-theories close to a critical point which falls in the Ising universality class. Here we show however that, even when critical, active particles strongly violate the equilibrium fluctuation-dissipation in the high-wave-vector and high-frequency regime. Conversely, at larger spatiotemporal scales the theorem is progressively restored and the critical dynamics is in effective equilibrium. We develop a field-theoretical description of this scenario employing a space-time correlated noise field finding that the theory qualitatively captures the numerical results already at the Gaussian level. Moreover a dynamic renormalization group analysis shows that the correlated noise does not change the equilibrium critical exponents. Our results demonstrate that a correlated noise field is a fundamental ingredient to describe critical active matter at the coarse-grained level.
Active particles can display a critical behaviour indistinguishable from an equilibrium one. The authors numerically study an active particles system close to the motility-induced critical point, and demonstrate that a nonequilibrium coloured noise field captures the coarse-grained behaviour of the system.