  For the spherical model with nearest-neighbour interactions, the
microcanonical entropy s(e,m) is computed analytically in the thermodynamic
limit for all accessible values of the energy e and the magnetization m per
spin. The entropy function is found to be concave (albeit not strictly
concave), implying that the microcanonical and the canonical ensembles are
equivalent, despite the long-range nature of the spherical constraint the spins
have to obey. Two transition lines are identified in the (e,m)-plane,
separating a paramagnetic phase from a ferromagnetic and an antiferromagnetic
one. The resulting microcanonical phase diagram is compared to the more
familiar canonical one.
