Two-Dimensional Melting: From Liquid-Hexatic Coexistence to Continuous Transitions

The phase diagram of two-dimensional continuous particle systems is studied using the event-chain Monte Carlo algorithm. For soft disks with repulsive power-law interactions proportional to r(-n) with n greater than or similar to 6, the recently established hard-disk melting scenario (n -> infinity) holds: a first-order liquid-hexatic and a continuous hexatic-solid transition are identified. Close to n = 6, the coexisting liquid exhibits very long orientational correlations, and positional correlations in the hexatic are extremely short. For n less than or similar to 6, the liquid-hexatic transition is continuous, with correlations consistent with the Kosterlitz-Thouless-Halperin-Nelson-Young (KTHNY) scenario. To illustrate the generality of these results, we demonstrate that Yukawa particles likewise may follow either the KTHNYor the hard-disk melting scenario, depending on the Debye-Huckel screening length as well as on the temperature.