Kittel: possible states of magnetic

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The discussion revolves around confusion regarding a section in Kittel's "Thermal Physics" about the states of magnetic moments. The original poster expects magnetic moments to decrease in increments of one, while others clarify that the increments actually occur in twos due to the nature of magnetic poles. When a magnet is flipped, it loses a north pole and gains a south pole, which explains the even increments. The explanation emphasizes that combining two magnets can only yield even multiples or cancel out completely, thus preventing odd multiples. Overall, the section is deemed not poorly explained but rather requires a deeper understanding of magnetic interactions.
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I do not understand the attached picture excerpt from Kittel Thermal Physics (first sentence up to 'eqn' (7) ).

I would expect the moments to go down in increments of one, not two. I think the subsequent paragraph tries to explain why, although I am not sure this is indeed the purpose. Could anyone please shed some light on this horribly explained section?

Thanks!
 

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Is it maybe because when you flip a magnet you lose a north and also gain a south? If you just took one away it would decrease by one but you took away a north and added a south.
 
It's not horribly explained. Try arranging 2 magnets in a way that the net moment is +1. Their either combine to +/- 2 (NN, SS) or cancel to 0 (NS, SN). You can't get odd multiples.
 

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