Abstract
Turbulent vortex structures emerging in bacterial active fluids can be organized into regular vortex lattices by weak geometrical constraints such as obstacles. Here we show, using a continuum-theoretical approach, that the formation and destruction of these patterns exhibit features of a continuous second-order equilibrium phase transition, including long-range correlations, divergent susceptibility, and critical slowing down. The emerging vorticity field can be mapped onto a two-dimensional (2D) Ising model with antiferromagnetic nearest-neighbor interactions by coarse graining. The resulting effective temperature is found to be proportional to the strength of the nonlinear advection in the continuum model.
- Received 19 July 2021
- Revised 29 November 2021
- Accepted 6 January 2022
DOI:https://doi.org/10.1103/PhysRevLett.128.048004
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