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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.
Motivated by the recently developed duality between elasticity of a crystal and a symmetric tensor gauge theory by Pretko and Radzihovsky, we explore its classical analog, that is a dual theory of the dislocation-mediated melting of a two-dimensional
In small confined systems predictions for the melting point strongly depend on the choice of quantity and on the way it is computed, even yielding divergent and ambiguous results. We present a very simple quantity which allows to control these proble
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