  We introduce a phase-space representation for qubits and spin models. The
technique uses an SU(n) coherent state basis, and can equally be used for
either static or dynamical simulations. We review previously known definitions
and operator identities, and show how these can be used to define an
off-diagonal, positive phase-space representation analogous to the positive
P-function. As an illustration of the phase-space method, we use the example of
the Ising model, which has exact solutions for the finite temperature canonical
ensemble in two dimensions. We show how a canonical ensemble for an Ising model
of arbitrary structure can be efficiently simulated using SU(2) or atomic
coherent states. The technique utilizes a transformation from a canonical
(imaginary-time) weighted simulation to an equivalent unweighted real-time
simulation. The results are compared to the exactly soluble two-dimensional
case. We note that Ising models in one, two or three dimensions are potentially
achievable experimentally as a lattice-gas of ultra-cold atoms in optical
lattices. The technique is not restricted to canonical ensembles or to
Ising-like couplings. It is also able to be used for real-time evolution, and
for systems whose time-evolution follows a master-equation describing
decoherence and coupling to external reservoirs. The case of SU(n) phase-space
is used to describe n-level systems. In general, the requirement that
time-evolution is stochastic corresponds to a restriction to Hamiltonians and
master-equations that are quadratic in the group generators or generalized spin
operators.
