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Unformatted text preview: 2. Derive a general expression for S< S z i > for a spinS quantum antiferromagnet, in the quadratic spinwave approximation. Examine this equation in one, two, and three dimensions for simple cubic lattices and small wavevectors k . If S< S z i > diverges, then the spinwave theory fails. or what dimensions and temperatures is this the case (i.e. consider the form of your equation for T = 0 and T 6 = 0 for one, two and three dimensions. Hint, consider the sum over k for small k )? Why does the theory fail in these cases (the reason has to do with the validity of the starting point, reconsider the results of problem one)? or the threedimensional case, you may want to look at T. Oguchi, Phys. Rev. 117 117, (1960); however, note that this author goes into signiFcantly more detail than is required here. 1...
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 Fall '11
 Electrodynamics
 Magnetism

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