Ferromagnetic and antiferromagnetic order in bacterial vortex lattices

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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 [6-9,14] 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 [17-19]. 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.