Triangular Lattice Model of 2D Defect Melting

Abstract

We set up a harmonic lattice model for 2D defect melting which, in contrast to earlier simple-cubic models, lives on a triangular lattice. Integer-valued plastic defect gauge fields allow for the thermal generation of dislocations and disclinations. The model produces universal formulas for the melting temperature expressed in terms of the elastic constants, which are different from those derived for square lattices. They determine a Lindemann-like parameter for two-dimensional melting. In contrast to the square crystal which underwent a first-order melting transition, the triangular model melts in two steps. Our results are applied to the melting of Lennard-Jones and electron lattices.

13 pages, 5 eps figures, section VI modified

References in corpus (1)

• Defect Melting Models for Cubic Lattices and Universal Laws for Melting Temperatures

Cited by in corpus (14)

• On the metastability of the hexatic phase during the melting of two-dimensional charged particle solids
• Tearing Fractons
• Theory of vortex-lattice melting in a one-dimensional optical lattice
• Possible role of 3He impurities in solid 4He
• Polyhexatic and Polycrystalline States of Skyrmion Lattices
• Screening properties and phase transitions in unconventional plasmas for Ising-type quantum Hall states
• Defect induced melting of vortices in high-${\mathbf{T}}_{\mathbf{c}}$ superconductors: A model based on continuum elasticity theory
• Freezing of an unconventional two-dimensional plasma
• Lindemann Parameters for solid Membranes focused on Carbon Nanotubes
• Phase Diagram of Vortices in High-Tc Superconductors from Lattice Defect Model with Pinning
• Solid-Liquid Transition in a Skyrmion Matter
• Melting and Freezing of a Skyrmion Lattice
• Modelling two-dimensional Crystals with Defects under Stress: Superelongation of Carbon Nanotubes at high Temperatures
• Phase Diagram of Vortices in High-T_c Superconductors with a Melting Line in the deep H_{c2} Region