Abstract
It is demonstrated that the Lindemann's criterion of melting can be formulated for two-dimensional classical solids using statistical mechanics arguments. With this formulation the expressions for the melting temperature are equivalent in three and two dimensions. Moreover, in two dimensions the Lindemann's melting criterion essentially coincides with the Berezinskii-Kosterlitz-Thouless-Halperin-Nelson-Young melting condition of dislocation unbinding.
Highlights
It is demonstrated that the Lindemann’s criterion of melting can be formulated for two-dimensional classical solids using statistical mechanics arguments
The BKTHNY scenario operates in systems with sufficiently soft long-range
For steeply repulsive interactions the hard-disk melting scenario holds with a firstorder liquid-hexatic and a continuous hexatic-solid transition [27,28,29]
Summary
The famous Lindemann’s melting criterion [1] states that melting of a three-dimensional (3D) solid occurs when the square root of the particle mean-squared displacement (MSD) from the equilibrium position reaches a threshold value (roughly ∼0.1 of the interparticle distance). MSD diverges with system size in 2D crystalline and amorphous solids [4,30], the squared deviation of the difference between the positions of two particles remains finite [31] This can serve as a basis to construct modified Lindemann-like criteria of 2D melting. The purpose of this Rapid Communication is to demonstrate that the Lindemann’s melting criterion can be reformulated for 2D classical systems using statistical mechanics arguments. For the sake of simpler notation, high-symmetry crystals are considered, so that quantities such as MSD or sound velocities can be considered as isotropic to
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