A thermodynamically consistent theory of the ferro/paramagnetic transition

We propose a continuum theory describing the evolution of magnetization and temperature in a rigid magnetic body. The theory is based on a microforce balance, an energy balance, and an entropy imbalance. We advance the choice of a class of constitutive equations, consistent with the entropy imbalance, that appear appropriate to describe the phase transition taking place in a ferromagnet at the Curie point. By combining these constitutive equations with the balance laws, we formulate an initial-boundary value problem for the magnetization and temperature fields, and we prove existence of weak solutions.