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Consider you have an Ising lattice with a dominant up component out of thermal equilibrium, that's your initial state. The down spins want to flip up and align with the ups, and they'll do so until a thermal distribution is reached. While they flip, the overall magnetization increases. Does that create a current by induction? I haven't been able to find a good reference.

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According to Maxwell's equations, a changing magnetic field creates an electric field, not a current.

This effect would indeed happen, but the Ising model just doesn't contain it. It also assumes that you have "spins on a lattice", which also don't really exist in this form (in reality, they are electrons which belong to atoms in a crystal lattice), and there is a bucketload of other effects which are also not considered.

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I was thinking of an atomic lattice. What does the electric fields to electrons in the conducting band if not create a current? But you're right in that my question confuses both. In any case, do you have any sort of reference for whether or not magnetic induction is or isn't present? – WIMP Apr 8 '13 at 7:18
I'm quite sure that induction is present. I don't have a reference, but aren't the Maxwell equations enough for you? – Rafael Reiter Apr 8 '13 at 8:19
What I'm looking for is the Ising model coupled to the current, so that one can calculate the induction from the lattice parameters. Alternatively, has somebody just plainly measured it? I mean, is there some reference on this? See, it isn't really clear to me how local currents do or don't add up to a global one. – WIMP Apr 11 '13 at 8:14

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