Destabilisation of the hexatic phase in systems of hard disks by quenched disorder due to pinning on a lattice

We investigate the effect of quenched disorder on the melting mechanism of two-dimensional hard disks using large-scale event-driven molecular dynamics simulations. The two-stage melting scenario of a continuous solid-hexatic and a first-order hexatic-liquid transition for a 2D system of hard disks does not persist in the case of quenched disorder, which arises by pinning less than one percent of the particles on a triangular lattice. Based on the Halperin-Nelson-Young (HNY) renormalization group equation, we observe that a first-order solid-liquid transition preempts the Kosterlitz-Thouless-type solid-hexatic transition in a 2D system of hard disks with quenched disorder as the stiffness of the crystal is increased by the presence of pinned particles.