Universal structural properties of three-dimensional and two-dimensional melts

A brief overview of the key methods for analyzing the structure of three-dimensional (3D) matter is given by using as an example melts of simple model systems like Lennard-Jones, Yukawa, and inverse power law. The behavior of simple structural measures characterizing matter near the melting line is considered in fine detail, and their advantages and disadvantages are discussed. Some indicators that characterize liquid near the melt line are proposed, and their universality and applicability for determining structure of melts of real liquids are discussed. Finally, the structural properties of two-dimensional (2D) liquids are compared with 3D ones. For 2D systems, simple universal criteria of melting are proposed, and their universality is shown using as an example a Yukawa system.