  We present an exact diagonalisation study of bilayer quantum Hall systems at
a filling factor of two in the spherical geometry. We find the
high-Zeeman-coupling phase boundary of the broken symmetry canted
antiferromagnet is given exactly by previous Hartree-Fock mean-field theories,
but that the state's stability at weak Zeeman coupling has been qualitatively
overestimated. In the absence of interlayer tunneling, degeneracies occur
between total spin multiplets due to the Hamiltonian's invariance under
independent spin-rotations in top and bottom two-dimensional electron layers.
