Microcanonical entropy of the spherical model with nearest-neighbour interactions

For the spherical model with nearest-neighbour interactions, the microcanonical entropy s(ε,m) is computed analytically in the thermodynamic limit for all accessible values of the energy ε and the magnetization m per spin. The entropy is found to be a concave function, implying that the microcanonical and the canonical ensemble are equivalent, despite the long-range nature of the spherical constraint the spins have to obey. Two transition lines are identified in the (ε,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.