When I have two magnets and try to rotate them so they are parallel, I feel a strong repulsive force which definitely tries to rotate them to an antiparallel notation.
However, when examining spin Hamiltonians, we see that in ferromagnetic cases parallel spins are actually energetically favored. I assume the confusion arises because a north/south pole analogy cannot be made using spins. But I'm wondering, what is the actual physical explanation of ferromagnetism?
Why are parallel spins energetically favored in ferromagnets?