Abstract: The melting transition of the five different lattices of a bilayer crystal is studied using the Monte-Carlo (MC) technique. We found the surprising result that the square lattice has a substantial larger melting temperature as compared to the other lattice structures, which is a consequence of the specific topology of the temperature induced defects. A new melting criterion is formulated which we show to be universal for bilayers as well as for single layer crystals.

Abstract: The spectral properties of a classical two-dimensional (2D) cluster of charged particles which are confined by a quadratic potential are calculated. Using the method of Newton optimization we obtain the ground state and the metastable states. For a given configuration the eigenvectors and eigenfrequencies for the normal modes are obtained using the Householder diagonalization technique for the dynamical matrix whose elements are the second derivative of the potential energy. For small clusters the lowest excitation corresponds to an intershell rotation. Magic numbers are associated to clusters which are most stable against intershell rotation. For large clusters the lowest excitation is a vortex/anti-vortex pair.