Dynamics of rotlet's ensemble

We investigate a two-dimensional ensemble of spinners driven by a rotating magnetic field. We demonstrate that in the absence of any interactions except hydrodynamic forces, the ensemble remains disordered. However, the introduction of a repulsive interaction between the spinners induces ordering within the ensemble. Through numerical simulations, we observe that this ordering resembles a freezing phenomenon and can be characterized using a Lindemann criterion. The freezing occurs because during the ordering of the ensemble, the velocity fluctuations caused by the hydrodynamic interactions decay substantially.