🚀 go-pugleaf

Alison Chaiken writes:

    The $0.05 answer: The fundamental underlying cause of conduction
    electron "itinerant" ferromagnetism is the Pauli exclusion principle.
    In some sense the exclusion principle causes a repulsive force between
    electrons of the same energy and spin.  (This is really an indirect
    manifestation of the Coulomb repulsion between like charges.)

I don't understand the parenthetical remark.  The exclusion
principle applies even to uncharged fermions, no?

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    converse of the preceding statement is that if you have a low-density
    electron gas, there is an effective net force aligning the spins.

Is there a rough-and-ready intuitive explanation for this effect?  Naively,
it would seem that the exclusion principle would tend to *anti-align*
spins.  That is, if you want to pack all your electrons (bound and
conduction) into the lowest possible energy configuration, it would seem
that every occupied quantum state would be paired with another occupied
quantum state with opposite spin but all other quantum numbers the same.

Obviously this line of thought is too naive.  Is there a qualitative
explanation that shows how Pauli exclusion --> aligned spins?