Molecular dynamics study of water-like anomalies, hexatic melting, and quasicrystal formation in two-dimensional systems

In this work, we present a detailed molecular dynamics simulation study of the complete phase behaviour of two-dimensional fluids interacting via a two-step potential consisting of a square-shoulder within a square-well (SSSW) pair interaction. We show that small adjustments in the interaction range can either promote or suppress water-like anomalies, hexatic phases, and quasicrystalline structures. We focus on two representative models. Model 1 exhibits a hexatic phase and water-like anomalies, whereas Model 2 promotes quasicrystal formation. Both models reproduce characteristic features of two-dimensional systems, including vapour–liquid coexistence, compact solid phases, and rich polymorphism. Model 1 shows the presence of multiple solid phases, including low-density triangular (LDT), irregular honeycomb (IHC), square (S), and high-density triangular (HDT) structures. In contrast, Model 2 exhibits dodecagonal (QC12) and octadecagonal (QC18) quasicrystalline phases, as well as a deformed honeycomb (DHC) structure. By analyzing thermodynamic properties, such as pressure and isothermal compressibility, together with structural features including diffraction patterns, bond networks, radial distribution functions, and bond-orientational order parameters, we map the vapour–liquid, liquid–solid, and solid–solid transitions. Finally, we confirm the existence of a hexatic phase in Model 1 based on a combined analysis of bond-orientational and translational correlation functions, together with the probability distribution of the magnitude of the local bond-orientational order parameter. No evidence of a hexatic phase is found for Model 2.