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

Two-dimensional melting in simple atomic systems: continuous vs. discontinous melting