Nature of two-dimensional melting in simple atomic systems

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