  Self-organization of moving objects in hydrodynamic environments has recently
attracted considerable attention in connection to natural phenomena and living
systems. However, the underlying physical mechanism is much less clear due to
the intrinsically nonequilibrium nature, compared with self-organization of
thermal systems. Hydrodynamic interactions are believed to play a crucial role
in such phenomena. To elucidate the fundamental physical nature of many-body
hydrodynamic interactions at a finite Reynolds number, here we study a system
of co-rotating hard disks in a two-dimensional viscous fluid at zero
temperature. Despite the absence of thermal noise, this system exhibits rich
phase behaviours, including a fluid state with diffusive dynamics, a cluster
state, a hexatic state, a glassy state, a plastic crystal state and phase
demixing.We reveal that these behaviours are induced by the off-axis and
many-body nature of nonlinear hydrodynamic interactions and the finite time
required for propagating the interactions by momentum diffusion.
