Density affects the nature of the hexatic-liquid transition in two-dimensional melting of core-softened systems

We find that both continuous and discontinuous hexatic-liquid transitions can happen in the melting of two-dimensional solids of soft-core disks. For three typical model systems, Hertzian, harmonic, and Gaussian-core models, we observe the same scenarios. These systems exhibit reentrant crystallization (melting) with a maximum melting temperature $T_m$ happening at a crossover density $\rho_m$. The hexatic-liquid transition at a density smaller than $\rho_m$ is discontinuous. Liquid and hexatic phases coexist in a density interval, which becomes narrower with increasing temperature and tends to vanish approximately at $T_m$. Above $\rho_m$, the transition is continuous, in agreement with the Kosterlitz-Thouless-Halperin-Nelson-Young theory. For these soft-core systems, the nature of the hexatic-liquid transition depends on density (pressure), with the melting at $\rho_m$ being a plausible transition point from discontinuous to continuous hexatic-liquid transition.