Phase diagram of two-dimensional hard ellipses.

Abstract

We report the phase diagram of two-dimensional hard ellipses as obtained from replica exchange Monte Carlo simulations. The replica exchange is implemented by expanding the isobaric ensemble in pressure. The phase diagram shows four regions: isotropic, nematic, plastic, and solid (letting aside the hexatic phase at the isotropic-plastic two-step transition [E. P. Bernard and W. Krauth, Phys. Rev. Lett. 107, 155704 (2011)]). At low anisotropies, the isotropic fluid turns into a plastic phase which in turn yields a solid for increasing pressure (area fraction). Intermediate anisotropies lead to a single first order transition (isotropic-solid). Finally, large anisotropies yield an isotropic-nematic transition at low pressures and a high-pressure nematic-solid transition. We obtain continuous isotropic-nematic transitions. For the transitions involving quasi-long-range positional ordering, i.e., isotropic-plastic, isotropic-solid, and nematic-solid, we observe bimodal probability density functions. This supports first order transition scenarios.