Self-Consistent Moment-Conserving Decoupling Scheme and Its Application to the Heisenberg Ferromagnet

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Abstract
A critique of the moment-conserving decoupling (MCD) procedure for linearizing Green's-function equations of motion is presented. It is shown that in its unembellished form this procedure is equivalent to an algorithm for constructing the relevant spectral function from the knowledge of its frequency moments. The nonuniqueness of this algorithm is discussed. Moreover, the limitations of this algorithm for predicting those frequency-wave-vector-dependent line shapes to which hydrodynamic modes make an important contribution is noted. To overcome some of these difficulties, the concept of a self-consistent momentconserving decoupling procedure (SCMCD) is introduced. The SCMCD is then employed to study the behavior of the long-range order in a Heisenberg ferromagnet with nearest-neighbor exchange. The results in three dimensions are found to be similar to those following from the use of the random-phase approximation (RPA) and the Callen decoupling. In one and two dimensions, the spontaneous magnetization is found to be vanishing at all finite temperatures. For spin ½, the SCMCD turns out to be identical to the Green's-function decoupling recently proposed by Mubayi and Lange.