Prediction of the liquid-crystal phase behavior of hard right triangles from fourth-virial density-functional theories

We have used an extended Scaled-Particle Theory that incorporates four-body correlations through the fourth-order virial coefficient to analyse orientational properties of a fluid hard right-angle triangles. This has been analysed by computer simulation studies, with clear indications strong octatic present in liquid-crystal phase, although more symmetric order tetratic phase would seem be most plausible candidate. Standard theories based on second are unable reproduce this behaviour. Our theory predicts correlations, associated symmetry under global rotations oriented $45^{\circ}$, highly enhanced, but not enough give rise thermodynamically stable strict symmetry. discuss different scenarios improve theoretical understanding elusive intriguing fluid.