Density Affects the Nature of the Hexatic-Liquid Transition in Two-Dimensional Melting of Soft-Core 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.