First-order and continuous melting transitions in two-dimensional Lennard-Jones systems and repulsive disks

In two-dimensional Lennard-Jones (LJ) systems, a small interval of melting-mode switching occurs below which the melting occurs by first-order phase transitions in lieu of the melting scenario proposed by Kosterlitz, Thouless, Halperin, Nelson, and Young (KTHNY). The extrapolated upper bound for phase coexistence is at density rho similar to 0.893 and temperature T similar to 1.1, both in reduced LJ units. The two-stage KTHNY scenario is restored at higher temperatures, and the isothermal melting scenario is universal. The solid-hexatic and hexatic-liquid transitions in KTHNY theory, even so continuous, are distinct from typical continuous phase transitions in that instead of scale-free fluctuations, they are characterized by unbinding of topological defects, resulting in a special form of divergence of the correlation length: xi approximate to exp(b vertical bar T - T-c vertical bar(-nu)). Here such a divergence is firmly established for a two-dimensional melting phenomenon, providing a conclusive proof of the KTHNY melting. We explicitly confirm that this high-temperature melting behavior of the LJ system is consistent with the melting behavior of the r(-12) potential and that melting of the r(-n) potential is KTHNY-like for n <= 12 but melting of the r(-64) potential is first order; similar to hard disks. Therefore we suggest that the melting scenario of these repulsive potentials becomes hard-disk-like for an exponent in the range 12 < n < 64