  We investigate the characteristics of two dimensional melting in simple
atomic systems via isobaric-isothermal ($NPT$) and isochoric-isothermal ($NVT$)
molecular dynamics simulations with special focus on the effect of the range of
the potential on the melting. We find that the system with interatomic
potential of longer range clearly exhibits a region (in the $PT$ plane) of
(thermodynamically) stable hexatic phase. On the other hand, the one with
shorter range potential exhibits a first-order melting transition both in $NPT$
and $NVT$ ensembles. Melting of the system with intermediate range potential
shows a hexatic-like feature near the melting transition in $NVT$ ensemble, but
it undergoes an unstable hexatic-like phase during melting process in $NPT$
ensemble, which implies existence of a weakly first order transition. The
overall features represent a crossover from a continuous melting transition in
the cases of longer-ranged potential to a discontinuous (first order) one in
the systems with shorter and intermediate ranged potential. We also calculate
the Binder cumulants as well as the susceptibility of the bond-orientational
order parameter.
