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Ising-like Critical Behavior of Vortex Lattices in an Active Fluid

18.02.2022

A recent study of PTB 8.4 scientists together with theoretical physicists at TU Berlin just appeared in Physical Review Letters and uncovers a surprising similarity between the transition from ordered patterns to turbulence in an non-equilibrium active fluid with the well known Ising transition of two-dimensional magnets in equilibrium conditions.

Turbulent vortex structures emerging in bacterial active fluids can be organized into regular vortex lattices by weak geometrical constraints such as obstacles. Using a continuum-theoretical approach, it was shown 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. This provides a surprising analogy between destabilizing nonlinearities in systems far from equilibrium and thermal fluctuation in equilibrium systems that may be relevant for other active or driven systems exhibiting transitions between order and chaos.

  

Publication: Henning Reinken, Sebastian Heidenreich, Markus Bär and Sabine Klapp, Opens external link in new windowPhysical Review Letters 128, 048004 (2022)  (Opens external link in new windowarXiv)

 

Experts: Markus Bär (8.41), Sebastian Heidenreich (8.43