Universality of the close packing properties and markers of isotropic-to-tetratic phase change in quasi-one-dimensional superdisk fluid

We study equilibrium states and phases of a quasi-one-dimensional system of hard superdisks (anisotropic particles interpolating between disks and squares) where the centers of the particles are constrained to move on a line. A continuous change from a quasi-isotropic to a tetratic phase is found upon increasing the density. Somewhat unexpected, for isobaric states, systems with larger and more anisotropic particles in the tetratic phase are denser than systems with smaller and less anisotropic particles in a quasi-isotropic phase. Close packing behaviour is characterised by exponents describing the behaviour of the pressure, the angular fluctuations and the angular correlation length. We obtain two universal, shape-independent relations between them.