Kittel: possible states of magnetic

[Aziza]

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!

 

[omega_minus]

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.

 

[mikeph]

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.