An experimental study of the phases of hard squares

We study the phase diagram of hard squares in two dimensions using millimeter-sized square particles on a vibrated plate. The plate serves as a quasi-thermal noise source which generates translational and rotational diffusion of isolated particles. As area density increases, the spatial arrangement of the squares undergoes a transition from isotropic to phases with four- and six-fold ordering, and subsequently develops crystalline order. This succession of transitions in orientational and translational ordering is in qualitative agreement with recent simulations [C. Avenda\~no and F. Escobedo, Soft Matter 2012 (8) 4675].