  We present a molecular dynamics simulation study of the phase diagram and
melting scenarios of two-dimensional Hertzian spheres with exponent 7/2. We
have found multiple re-entrant melting of a single crystal with a triangular
lattice in a wide range of densities from 0.5 to 10.0. Depending on the
position on the phase diagram, the triangular crystal has been shown to melt
through both two-stage melting with a first-order hexatic - isotropic liquid
transition and a continuous solid - hexatic transition as well as in accordance
with the Berezinskii-Kosterlitz-Thouless-Halperin-Nelson-Young (BKTHNY)
scenario (two continuous transitions with an intermediate hexatic phase). We
studied the behavior of heat capacity and have shown that despite two-stage
melting, the heat capacity has one peak which seems to correspond to a
solid-hexatic transition.
