Further Series Studies of the Spin-1/2 Heisenberg Antiferromagnet at T=0: Magnon Dispersion and Structure Factors

We have extended our previous series studies of quantum antiferromagnets at zero temperature by computing the one-magnon dispersion curves and various structure factors for the linear chain, square and simple cubic lattices. Many of these results are new; others are a substantial extension of previous work. These results are directly comparable with neutron scattering experiments and we make such comparisons where possible.Comment: 15 pages, 12 figures, revised versio

Spin-wave excitation spectra and spectral weights in square lattice antiferromagnets

Using a recently developed method for calculating series expansions of the excitation spectra of quantum lattice models, we obtain the spin-wave spectra for square lattice, $S=1/2$ Heisenberg-Ising antiferromagnets. The calculated spin-wave spectrum for the Heisenberg model is close to but noticeably different from a uniformly renormalized classical (large-$S$) spectrum with the renormalization for the spin-wave velocity of approximately $1.18$. The relative weights of the single-magnon and multi-magnon contributions to neutron scattering spectra are obtained for wavevectors throughout the Brillouin zone.Comment: Two postscript figures, 4 two-column page

A characterization of the central shell-focusing singularity in spherical gravitational collapse

We give a characterization of the central shell-focusing curvature singularity that can form in the spherical gravitational collapse of a bounded matter distribution obeying the dominant energy condition. This characterization is based on the limiting behaviour of the mass function in the neighbourhood of the singularity. Depending on the rate of growth of the mass as a function of the area radius R, the singularity may be either covered or naked. The singularity is naked if this growth rate is slower than R, covered if it is faster than R, and either naked or covered if the growth rate is same as R.Comment: 12 pages, Latex, significantly revised version, including change of title. Revised version to appear in Classical and Quantum Gravit