Note: Melting criterion for soft particle systems in two dimensions

Abstract

A simple criterion for melting of two-dimensional crystals with soft long-ranged interactions is proposed. It states that the ratio of the transverse sound velocity of an ideal crystalline lattice to the thermal velocity is a quasi-universal number close to $4.3$ at melting. This criterion is arrived by reference to the Berezinskii-Kosterlitz-Thouless-Halperin-Nelson-Young theory of two-dimensional melting, combined with the observation that the ratio of transverse-to-longitudinal sound velocities is small in the soft interaction limit. Application of this criteria allows estimating melting lines in a simple yet relatively accurate manner. Two-dimensional weakly screened Yukawa systems represent one relevant example considered.

2 pages note in JCP

References in corpus (7)

• 2D Melting: From Liquid-Hexatic Coexistence to Continuous Transitions
• Dynamical correlations and collective excitations of Yukawa liquids
• Collective modes in simple melts: Transition from soft spheres to the hard sphere limit
• Thermodynamics of two-dimensional Yukawa systems across coupling regimes
• Thermodynamics and dynamics of two-dimensional systems with dipole-like repulsive interactions
• Internal energy of the classical two- and three-dimensional one-component-plasma
• High-frequency elastic moduli of two-dimensional Yukawa fluids and solids

Cited by in corpus (10)

• Lindemann melting criterion in two dimensions
• Collective modes of two-dimensional classical Coulomb fluids
• Sound velocities of Lennard-Jones systems near the liquid-solid phase transition
• Unified description of sound velocities in strongly coupled Yukawa systems of different spatial dimensionality
• Two-body entropy of two-dimensional fluids
• The boundary density profile of a Coulomb droplet. Freezing at the edge
• Elastic properties of dense hard-sphere fluids
• When do soft spheres become hard spheres?
• Note: Sound velocities of generalized Lennard-Jones ($n-6$) fluids near freezing
• Vibrational model of entropy in dense two-dimensional fluids