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Despite their inherent non-equilibrium nature, living systems canself-organize in highly ordered collective states that share strikingsimilarities with the thermodynamic equilibrium phases of conventionalcondensed matter and fluid systems. Examples range from the liquid-crystal-likearrangements of bacterial colonies, microbial suspensions and tissues to thecoherent macro-scale dynamics in schools of fish and flocks of birds. Yet, thegeneric mathematical principles that govern the emergence of structure in suchartificial and biological systems are elusive. It is not clear when, or evenwhether, well-established theoretical concepts describing universalthermostatistics of equilibrium systems can capture and classify ordered statesof living matter. Here, we connect these two previously disparate regimes:Through microfluidic experiments and mathematical modelling, we demonstratethat lattices of hydrodynamically coupled bacterial vortices can spontaneouslyorganize into distinct phases of ferro- and antiferromagnetic order. Thepreferred phase can be controlled by tuning the vortex coupling through changesof the inter-cavity gap widths. The emergence of opposing order regimes istightly linked to the existence of geometry-induced edge currents, reminiscentof those in quantum systems. Our experimental observations can be rationalizedin terms of a generic lattice field theory, suggesting that bacterial spinnetworks belong to the same universality class as a wide range of equilibriumsystems.

Ferromagnetic and antiferromagnetic order in bacterial vortex lattices