The spontaneous emergence and destruction of crystal-like order can be observed in a wide variety of natural and artificial systems 2, 7, 8, 9, 10. In contrast to equilibrium crystals, active non-equilibrium crystals can both self-assemble 2, 3 and melt into an active fluid 4, 5, 6, owing to the intrinsic motility of their microscopic constituents. It remains an open question, however, to which extent such transitions generalize to crystallization and melting phenomena in active systems. Melting of 2D crystal structures has played a pivotal role for our understanding of order-disorder transitions in equilibrium systems 1. Generally, these results highlight the differences and similarities between crystalline phases in active fluids and their equilibrium counterparts. The melting of this crystal proceeds through an intermediate hexatic phase. On large domains, an active vortex crystal with solid order forms within the parameter range corresponding to active vortex lattices. On small domains, we identify a hysteretic transition as well as a transition featuring temporal coexistence of active vortex lattices and active turbulence, both of which can be controlled by self-propulsion and active stresses. Performing extensive hydrodynamic simulations, we find rich transition scenarios. Here, we establish the emergence and investigate the melting of self-organized vortex crystals in 2D active fluids using a generalized Toner-Tu theory. Currently, the non-equilibrium physics of active crystallization and melting processes is not well understood. In contrast to passive systems, active crystals can self-assemble and melt into an active fluid by virtue of their intrinsic motility and inherent non-equilibrium stresses. Melting of two-dimensional (2D) equilibrium crystals is a complex phenomenon characterized by the sequential loss of positional and orientational order.
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