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Unformatted text preview: 2. Derive a general expression for S-< S z i > for a spin-S quantum antiferromagnet, in the quadratic spin-wave 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 spin-wave 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 three-dimensional 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