The magnetocaloric effect in materials with a second order phase transition: Are TC and Tpeak necessarily coincident?

Using the Arrott–Noakes equation of state it is shown that the Curie point (TC) and the temperature where the magnetic entropy change is maximum (Tpeak) coincide only in the mean field approximation, but the Heisenberg model implies that Tpeak>TC even for homogeneous materials. The distance between Tpeak and TC increases with applied magnetic field following a power law. In both cases, TC corresponds to a singular point in the temperature dependence of the magnetic entropy change. The field dependence of the magnetic entropy change is exactly the same at the Curie temperature and at the temperature of the peak.