  In this article, new results are presented for the zero-temperature
ground-state properties of the spin-half transverse Ising model on various
lattices using three different approximate techniques. These are, respectively,
the coupled cluster method, the correlated basis function method, and the
variational quantum Monte Carlo method. The methods, at different levels of
approximation, are used to study the ground-state properties of these systems,
and the results are found to be in excellent agreement both with each other and
with results of exact calculations for the linear chain and results of exact
cumulant series expansions for lattices of higher spatial dimension. The
different techniques used are compared and contrasted in the light of these
results, and the constructions of the approximate ground-state wave functions
are especially discussed.
