  It is shown that at low densities, quantum dots with few electrons may be
mapped onto effective charge-spin models for the low-energy eigenstates. This
is justified by defining a lattice model based on a many-electron pocket-state
basis in which electrons are localised near their classical ground-state
positions. The equivalence to a single-band Hubbard model is then established
leading to a charge-spin ($t-J-V$) model which for most geometries reduces to a
spin (Heisenberg) model. The method is refined to include processes which
involve cyclic rotations of a ``ring'' of neighboring electrons. This is
achieved by introducing intermediate lattice points and the importance of ring
processes relative to pair-exchange processes is investigated using high-order
degenerate perturbation theory and the WKB approximation. The energy spectra
are computed from the effective models for specific cases and compared with
exact results and other approximation methods.
