Second order phase transitions and energy

Apologies if I am missing something simple here. We are all aware that a latent heat is associated with a 1st order phase transition. The heat released on cooling is associated with the change in energy of the system as it transitions to its new phase. The order parameter jumps discontinuously at Tc and then perhaps changes more slowly as the temperature is lowered further.

No latent heat is associated with a second order phase transition. The order parameter changes continuously from zero at Tc. So for example, in a ferromagnetic material, spins begin lining up at Tc until at 0C, all are lined up (I realize there are domains in a real material that are not aligned in the same direction – I’m ignoring this). Or in a superconductor (in zero magnetic field), the gap opens at Tc and grows to its full size at 0C.

Both of these types of phase transitions herald the transition of the system to a lower energy configuration. In a first order transition, we can use a calorimeter to measure the latent heat. But there is no rapid release of heat to measure with a second order transition. So my question is this:

In systems that undergo second order phase transitions,

• Are these systems slowly radiating away energy as they cool below Tc to attain the lower energy configuration, or

• Is there just a realignment of the total system energy between the potential and kinetic terms?

I was made aware of the possibility of the latter through reading the abstract of this paper on ferromagnetism: Phys. Rev. B 90, 125102 (2014).

In the abstract the authors write: "In the conventional Stoner-Wohlfarth model, and in spin-polarized LDA calculations, the ferromagnetic ordering of iron sets in so that the electrons can reduce their mutual Coulomb repulsion, at the cost of some increase of electron kinetic energy."

So for ferromagnetic iron, it would seem the second of the two choices above is what is happening. If I am indeed understanding this correctly, is this also generally true for other second order transitions?

Thanks for your thoughts on the subject!

Edit: Thinking about this some more, I recalled that second order phase transitions are characterized by a large jump in heat capacity at Tc, which then drops in a lambda shape as temperature is cooled. It seems logical that the increase in energy that must be removed from the sample to cool the sample once below Tc would be associated with the energy needed to continuously move the system into the new phase, though I have never seen it phrased that way. Again, thanks for any thoughts.