  We report microcanonical Monte Carlo simulations of melting and superheating
of a generic, Lennard-Jones system starting from the crystalline phase. The
isochoric curve, the melting temperature $T_m$ and the critical superheating
temperature $T_{LS}$ obtained are in close agreement (well within the
microcanonical temperature fluctuations) with standard molecular dynamics
one-phase and two-phase methods. These results validate the use of
microcanonical Monte Carlo to compute melting points, a method which has the
advantage of only requiring the configurational degrees of freedom. Our
findings show that the strict preservation of the Hamiltonian dynamics does not
constitute a necessary condition to produce a realistic estimate of $T_{LS}$
and the melting point, which brings new insight on the nature of the melting
transition. These results widen the use and applicability of the recently
developed Z method for the determination of the melting points of materials.
