Selfconsistent theory of the thermal softening and instability of simple crystals
Abstract
We consider the thermal softening of crystals due to anharmonicity. Selfconsistent methods find a maximum temperature for a stable crystal, which gives an upper bound to the melting temperature. Previous workers have shown that the selfconsistent harmonic approximation (SCHA) gives misleading results for the thermal stability of crystals. The reason is that the most important diagrams in the perturbation expansion around harmonic theory are not included in the SCHA. An alternative approach is to solve a selfconsistent Dyson equation (SCA) for a selection of diagrams, the simplest being a (3+4)SCA. However, this gives an unsatisfactory comparison to numerical results on the thermal and quantum melting of twodimensional (2D) Coulombinteracting particles (equivalent to vortexlattice melting in two and three dimensions). We derive an improved selfconsistent method, the twovertexSCHA, which gives much better agreement to the simulations. Our method allows for accurate calculation of the thermal softening of the shear modulus for 2D crystals and for the lattice of vortexlines in typeII superconductors.
 Publication:

arXiv eprints
 Pub Date:
 July 2000
 arXiv:
 arXiv:condmat/0007072
 Bibcode:
 2000cond.mat..7072D
 Keywords:

 Condensed Matter  Statistical Mechanics;
 Condensed Matter  Soft Condensed Matter;
 Condensed Matter  Superconductivity
 EPrint:
 17 pages, 11 figures