On the behavior of indicators of melting: Lennard-Jones system in the vicinity of the phase transition

Various indicators of melting for a system of particles whose pair interaction is described by the Lennard-Jones potential have been considered. The behavior of the radial distribution function $g(r)$ and the associated criteria of melting, modified Lindemann criterion, and criteria based on the properties of short-range orientational order (rotational invariants $q_l$ and $w_l$ of various orders $l$) has been analyzed in detail in the vicinity of the melting phase transition. A parameter based on the loss of the nearest neighbors of an atom/particle has been proposed to characterize the melting transition. All considered indicators of melting for the Lennard-Jones system have been compared. It has been shown that the indicators of melting derived from the properties of the short-range orientational order are much more sensitive to the melting phase transition and can be used to construct new phenomenological criteria of melting similar to the Lindemann criterion. An additional important advantage of such indicators is the relatively small number of configurations of the system necessary for their calculation.