Brownian motion

Physics

Universality (dynamical systems)

Mathematics

Mathematical physics

Renormalization group

Non-equilibrium thermodynamics

Statistical physics

Phase transition

Critical exponent

Mathematical analysis

Critical phenomena

Critical point (mathematics)

Geometry

Condensed matter physics

Ising model

Quantum mechanics

Thermodynamics

Scaling

Physical review. E

We study active Brownian particles as a paradigm for a genuine nonequilibrium phase transition requiring steady driving. Access to the critical point in computer simulations is obstructed by the fact that the density is conserved. We propose a method based on arguments from finite-size scaling to determine critical points and successfully test it for the two-dimensional (2D) Ising model. Using this method allows us to accurately determine the critical point of two-dimensional active Brownian particles at ${\mathrm{Pe}}_{\text{cr}}=40(2), {\ensuremath{\phi}}_{\text{cr}}=0.597(3)$. Based on this estimate, we study the corresponding critical exponents $\ensuremath{\beta}, \ensuremath{\gamma}/\ensuremath{\nu}$, and $\ensuremath{\nu}$. Our results are incompatible with the 2D-Ising exponents, thus raising the question whether there exists a corresponding nonequilibrium universality class.

Critical behavior of active Brownian particles