Speaker
Description
The renormalization group starts from an effective field theory -- but where does that theory come from? In hydrodynamics, the relevant degrees of freedom and symmetries can themselves emerge at long wavelengths. The Navier–Stokes equation provides a paradigmatic example: conservation laws and emergent symmetries strongly constrain the form of the long-wavelength theory, largely independently of microscopic details.
Far from equilibrium, this hydrodynamic viewpoint becomes particularly fertile. Unshackled by detailed balance, the space of allowed dynamical theories expands dramatically: new nonlinearities become possible, emergent symmetries can arise, and RG fixed points and universality classes (UCs) proliferate [1].
I will illustrate these ideas using active matter. I will first discuss the ordered phase of polar flocks [2–6], where emergent symmetries strongly constrain the RG flow and can lead to exact scaling relations. I will then turn to the critical behaviour of active Ising models, where nonequilibrium couplings generate a remarkably rich fixed-point structure, including a new UC that supersedes the equilibrium Wilson–Fisher UC as the generic description of the critical transition [7].
These examples highlight two complementary challenges for RG far from equilibrium: constructing the appropriate long-wavelength theory and tackling the proliferation of nonlinearities that arises once the constraints of equilibrium are lifted. I will conclude by asking whether functional RG approaches can help address the latter challenge.
[1] P. Jentsch and C. F. Lee, Hydrodynamics, Renormalization Group, and Universality Classes Far from Equilibrium, arXiv:2607.02318.
[2] L. Chen, C. F. Lee, and J. Toner, Mapping two-dimensional polar active fluids to two-dimensional soap and one-dimensional sandblasting, Nat. Commun. 7, 12215 (2016).
[3] L. Chen, C. F. Lee, and J. Toner, Incompressible polar active fluids in the moving phase in dimensions d > 2, New J. Phys. 20, 113035 (2018).
[4] L. Chen, C. F. Lee, and J. Toner, Moving, Reproducing, and Dying Beyond Flatland: Malthusian Flocks in Dimensions d > 2, Phys. Rev. Lett. 125, 098003 (2020).
[5] L. Chen, C. F. Lee, A. Maitra, and J. Toner, Dynamics of packed swarms: Time-displaced correlators of two-dimensional incompressible flocks, Phys. Rev. E 109, L012601 (2024).
[6] P. Jentsch and C. F. Lee, New Universality Class Describes Vicsek’s Flocking Phase in Physical Dimensions, Phys. Rev. Lett. 133, 128301 (2024).
[7] M. Wong and C. F. Lee, New Universality Classes Govern the Critical and Multicritical Behavior of an Active Ising Model, arXiv:2507.06068.
| Affiliation | Imperial College London |
|---|---|
| Link to paper | https://arxiv.org/abs/2607.02318 |
| Career status | Senior |