  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.
