Phase behavior of hard circular arcs

By using Monte Carlo numerical simulation, this work investigates the phase behavior of systems of hard infinitesimally-thin circular arcs, from an aperture angle $\theta \rightarrow 0$ to an aperture angle $\theta \rightarrow 2 \pi$, in the two-dimensional Euclidean space. Except in the isotropic phase at lower density and in the (quasi)nematic phase that solely forms for sufficiently small values of $\theta$ and at intermediate values of density, in the other phases that form, including the isotropic phase at higher density, hard infinitesimally-thin circular arcs auto-assemble to form clusters. These clusters are either filamentous, for smaller values of $\theta$, or roundish, for larger values of $\theta$. Provided density is sufficiently high, the filaments lengthen, merge and straighten to finally produce a filamentary phase while the roundels compact and dispose themselves with their centers of mass at the sites of a triangular lattice to finally produce a cluster hexagonal phase.