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An exact perturbation expansion, to the order 1/S 2 , is derived for the Heisenberg ferromagnet. The equivalence of the Dyson-Maleev (DM), Holstein-Primakoff (HP) and matching-of-matrix-element (MME) transformations is proven. They give identical T 5/2 and T 4 coefficients. For the planar ferromagnet, an exact expansion in anisotropy against exchange field proves the equivalence of the HP and MME transformations. Several explicit results and numerical estimates are given.
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E. Rastelli (1979) studied this question.
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