  In this paper we revisit the onset of the instability of the solid state in
classical systems within self-consistent phonon theory (SCPT). Spanning the
whole phase diagram versus volume and versus pressure, we identify two
different kinds of mechanism: one mainly relevant at constant volume,
associated with the vanishing of the SCPT solution; and one related to the
disappearing at a spinodal temperature of the solid phase as a metastable
energy minimum. We show how the first mechanism occurs at extremely high
temperatures and it is not reflected in any singular behavior of the
thermodynamical properties. In contrast, the second one appears at physical
temperatures which correlate well with the melting temperature and it is
signalized by the divergence of the thermal compressibility as well as of the
the lattice expansion coefficient.
