  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.
