Ferromagnetic and antiferromagnetic order in bacterial vortex lattices

Hydrodynamic coupling induces a vortex state in bacterial populations. Microfluidic experiments and modelling now demonstrate that lattices of these vortices can self-organize into patterns characterized by ferro- and antiferromagnetic order. Despite their inherently non-equilibrium nature 1 , living systems can self-organize in highly ordered collective states 2 , 3 that share striking similarities with the thermodynamic equilibrium phases 4 , 5 of conventional condensed-matter and fluid systems. Examples range from the liquid-crystal-like arrangements of bacterial colonies 6 , 7 , microbial suspensions 8 , 9 and tissues 10 to the coherent macro-scale dynamics in schools of fish 11 and flocks of birds 12 . Yet, the generic mathematical principles that govern the emergence of structure in such artificial 13 and biological 6 , 7 , 8 , 9 , 14 systems are elusive. It is not clear when, or even whether, well-established theoretical concepts describing universal thermostatistics of equilibrium systems can capture and classify ordered states of living matter. Here, we connect these two previously disparate regimes: through microfluidic experiments and mathematical modelling, we demonstrate that lattices of hydrodynamically coupled bacterial vortices can spontaneously organize into distinct patterns characterized by ferro- and antiferromagnetic order. The coupling between adjacent vortices can be controlled by tuning the inter-cavity gap widths. The emergence of opposing order regimes is tightly linked to the existence of geometry-induced edge currents 15 , 16 , reminiscent of those in quantum systems 17 , 18 , 19 . Our experimental observations can be rationalized in terms of a generic lattice field theory, suggesting that bacterial spin networks belong to the same universality class as a wide range of equilibrium systems.