In the wiki article phase transition, the ferromagnetic phase transition is listed both in Ehrenfest second order phase transition and continuous phase transition in modern classification. Is there a contradiction?
Since according to the article:
Though useful, Ehrenfest's classification has been found to be an incomplete method of classifying phase transitions, for it does not take into account the case where a derivative of free energy diverges (which is only possible in the thermodynamic limit).
From this, I conclude that ferromagnetic phase transition should not have divergent susceptibility since it is in the second order phase transition in Ehrenfest classification.
But below this the article also writes:
...continuous phase transitions. They are characterized by a divergent susceptibility, an infinite correlation length, and a power-law decay of correlations near criticality. Examples of second-order phase transitions are the ferromagnetic transition...
From this, I will conclude that ferromagnetic phase transition has divergent susceptibility.
How to reconcile these two statement?
If we accept that a divergent derivative is discontinuous, then Ehrenfest classification is perfectly OK, all the phase transition can be classified, why not adopt this convention but invent a new classification method?