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arXiv · 2107.11130

Ising-like critical behavior of vortex lattices in an active fluid

Henning Reinken·Sebastian Heidenreich·Markus Bär·Sabine H. L. Klapp
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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.

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Henning Reinken, Sebastian Heidenreich, Markus Bär, Sabine H. L. Klapp. 2022-01-28. Ising-like critical behavior of vortex lattices in an active fluid. https://doi.org/10.1103/physrevlett.128.048004

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