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

TL;DR

This paper demonstrates that vortex lattice formation in bacterial active fluids exhibits critical behavior akin to a 2D Ising model phase transition, with long-range correlations and divergent susceptibility.

Contribution

It introduces a continuum-theoretical framework linking vortex patterns in active fluids to Ising-like critical phenomena, revealing a new universality class.

Findings

Vortex lattice formation shows features of a second-order phase transition.

The vorticity field maps onto a 2D Ising model with antiferromagnetic interactions.

Effective temperature correlates with nonlinear advection strength.

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.