  This paper studies a generalization of the Curie-Weiss model (the Ising model
on a complete graph) to quantum mechanics. Using a natural probabilistic
representation of this model, we give a complete picture of the phase diagram
of the model in the parameters of inverse temperature and transverse field
strength. Further analysis computes the critical exponent for the decay of the
order parameter in the approach to the critical curve and gives useful
stability properties of a variational problem associated with the
representation.
