  We discuss the d=2 quantum O(2)xO(2) nonlinear sigma model as a low-energy
theory of phase reconstruction near a quantum critical point. We first examine
the evolution of the Berezinskii-Kosterlitz-Thouless (BKT) transition as the
quantum limit is approached in the usual O(2) nonlinear sigma model. Then we go
on to review results on the ground-state phase diagram of the O(2)xO(2)
nonlinear sigma model, and on the behaviour of the O(2)xO(M) nonlinear sigma
model with M>2 in the classical limit. Finally, we present a conjectured
finite-temperature phase diagram for the quantum version of the latter model in
the O(2)xO(2) case. The nature of the finite-temperature BKT-like transitions
in the phase diagram is discussed, and avenues for further calculation are
identified.
