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We find that both continuous and discontinuous hexatic-liquid transitions canhappen in the melting of two-dimensional solids of soft-core disks. For threetypical model systems, Hertzian, harmonic, and Gaussian-core models, we observethe 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 $\rho_m$ isdiscontinuous. Liquid and hexatic phases coexist in a density interval, whichbecomes narrower with increasing temperature and tends to vanish approximatelyat $T_m$. Above $\rho_m$, the transition is continuous, in agreement with theKosterlitz-Thouless-Halperin-Nelson-Young theory. For these soft-core systems,the nature of the hexatic-liquid transition depends on density (pressure), withthe melting at $\rho_m$ being a plausible transition point from discontinuousto continuous hexatic-liquid transition.

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