In pursuit of the tetratic phase in hard rectangles

We numerically investigate two-dimensional systems of hard rectangles at constant pressure through extensive hard-particle Monte Carlo simulations. We determine the complete phase diagram as a function of packing fraction and aspect ratio, which consists of four distinct phases. At very high packing fractions, particles assemble into a smectic phase for all aspect ratios. Rodlike particles with large aspect ratio assemble into an intervening nematic phase, which is displaced by a “tetratic” phase (also called biaxial nematic) for moderately elongated rectangles. Surprisingly, we find evidence that the transition from tetratic to smectic is weakly discontinuous at variance with previously proposed two-step scenarios for the melting of hard particles.