Ground states of two typical many-boson model systems are studied: (i) a weakly interacting boson system at low density, and (ii) a low-density hard-sphere boson gas in the low-energy limit. For both of these systems it is shown explicitly that the uniform-limit formalism based on the method of correlated basis functions can be used to obtain, in a relatively simple way, exact results for the ground-state energy per particle and other related properties in the weak-coupling limit. In the problem of the hard-sphere boson gas the
T-matrix method is found to be particularly useful in dealing with the singular interaction potential.
We use exact diagonalization in order to study the infinite-U limit of the two-dimensional Hubbard model. As well as looking at single-particle correlations, such as ${\mathit{n}}_{\mathit{k}\mathrm{\ensuremath{\sigma}}}$=〈${\mathit{c}}_{\mathit{k}\mathrm{\ensuremath{\sigma}}}^{\mathrm{\ifmmode^\circ\else\textdegree\fi{}}}$${\mathit{c}}_{\mathit{k}\mathrm{\ensuremath{\sigma}}}$〉, we also study N-particle correlation functions, which compare the relative positions of all the particles in different models. In particular we study 16- and 18-site clusters and compare the charge correlations in the Hubbard model with those of spinless fermions and hard-core bosons. We find that although low densities of holes favor a ``locally ferromagnetic'' fermionic description, the correlations at larger densities resemble those of pure hard-core bosons surprisingly well.