The paramagnetic/ferromagnetic phase transition is an archetypal example of a continuous (or second-order) phase transition. When the temperature $T$ approaches the Curie temperature $T_c$, the magnetization $M(T)$, which is the order parameter of the transition, continuously goes to zero.
I heard (in an informal context) that under a constant nonzero magnetic field $H$, the transition becomes first order, but I was not able to find references which clearly confirm or infirm this statement, and I am not convinced of any of the possibilities.
So my question is : is the paramagnetic/ferromagnetic transition under magnetic field, $H\neq 0$, a continuous or a first order transition ? (It would be better with a reference, but I would also like an explanation.)
Thanks in advance.