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

Area of Science:

• Physics of complex fluids
• Soft matter physics
• Statistical mechanics

Background:

• Turbulent vortex structures arise spontaneously in bacterial active fluids.
• Geometrical constraints, like obstacles, can organize these vortices into regular patterns.
• Understanding the collective behavior and phase transitions in such active matter is crucial.

Purpose of the Study:

• To investigate the nature of pattern formation and destruction in bacterial active fluids under geometrical constraints.
• To determine if these pattern dynamics exhibit characteristics of a continuous phase transition.
• To establish a theoretical framework connecting the fluid's vorticity field to established statistical models.

Main Methods:

• A continuum-theoretical approach was employed to model the bacterial active fluid.
• Analysis focused on the formation and destruction dynamics of vortex lattices.
• The vorticity field was coarse-grained and mapped onto a two-dimensional (2D) Ising model.

Main Results:

• The formation and destruction of vortex patterns display hallmarks of a continuous second-order equilibrium phase transition.
• Observed features include long-range correlations, divergent susceptibility, and critical slowing down.
• The vorticity field effectively maps to a 2D Ising model with antiferromagnetic interactions.
• The emergent effective temperature is directly proportional to the nonlinear advection strength.

Conclusions:

• Bacterial active fluid systems can undergo continuous phase transitions analogous to equilibrium systems.
• The 2D Ising model provides a powerful framework for understanding emergent order in active matter.
• Nonlinear advection plays a key role in determining the effective temperature and critical behavior of these systems.