We use an optimised hopping parameter expansion for the free energy (linear δ-expansion) to study the phase transitions at finite temperature and finite charge density in a global U(1) scalar Higgs sector on the lattice at large lattice couplings. We are able to plot out phase diagrams in lattice parameter space and find that the standard second-order phase transition with temperature at zero chemical potential becomes first order as the chemical potential increases.

We apply the linear delta expansion to the quantum mechanical version of the slow rollover transition which is the principal feature of inflationary models of the early Universe. The method, which goes beyond the Gaussian approximation, gives results which stay close to the exact solution for longer than previous methods. It provides a promising basis for extension to a full field theoretic treatment.

We use an optimized hopping parameter expansion (linear \delta expansion) for the free energy to study the phase transitions at finite temperature and finite charge density in a global U(1) scalar Higgs sector in the continuum and on the lattice at large couplings. We are able to plot out phase diagrams in lattice parameter space and find that the standard second-order phase transition with temperature at zero chemical potential becomes first-order as the chemical potential increases.

The phonon dispersion relation has been measured for sodium chloride at room temperature for waves propagating along the symmetry directions [00ζ], [ζζ0], and [ζζζ] by slow neutron inelastic scattering using the Materials Testing Reactor three axis spectrometer. These data are in reasonable agreement with the low temperature (80°K) data obtained by Almqvist et al. and with the X-ray scattering data of Buyers and Smith. The shell model has been fit to the present data using a non-linear least squares routine with the fourteen parameter version giving the best overall agreement when the fitting to the elastic constants is also included. In the text comparison is made with a seven parameter rigid-ion model along with eleven and fourteen parameter versions of the shell model. The fourteen parameter shell model has been applied in calculating a frequency distribution from which the Debye temperature was evaluated for comparison with thermodynamic data, and the combined density-of-states distribution was computed and compared with second order Raman scattering data, both with good agreement.