  We consider a two-dimensional electron or hole system at zero temperature and
low carrier densities, where the long-range Coulomb interactions dominate over
the kinetic energy. In this limit the clean system will form a Wigner crystal.
Non-trivial quantum mechanical corrections to the classical ground state lead
to multiparticle exchange processes that can be expressed as an effective spin
Hamiltonian involving competing interactions. Disorder will destroy the Wigner
crystal on large length scales, and the resulting state is called a Wigner
glass. The notion of multiparticle exchange processes is still applicable in
the Wigner glass, but the exchange frequencies now follow a random
distribution. We compute the exchange frequencies for a large number of
relevant exchange processes in the Wigner crystal, and the frequency
distributions for some important processes in the Wigner glass. The resulting
effective low energy spin Hamiltonian should be the starting point of an
analysis of the possible ground state phases and quantum phase transitions
between them. We find that disorder plays a crucial role and speculate on a
possible zero temperature phase diagram.
