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I'm preparing a short presentation about the Kondo effect. I'm going to talk about the Anderson model and then Kondo's approach to deriving the logarithmic term using perturbation theory.

Here's my question: why is it important that the spin of the impurity flips?

I understand that the impurity electron can be "replaced" by a conduction electron, and that impurity electron then acquires an energy at the Fermi surface. This happens several times, and since resistivity is governed by the amount of electrons within ~kT of the Fermi edge, the resistivity goes up. However, I don't understand why the orientation of the spin matters. For more background, I haven't taken solid state physics before, and this is actually for a quantum class (hence the focus on perturbation theory).

Thank you in advance for your help.