Spin fluctuation theory in condensed quantum systems

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Abstract
This review deals with spin fluctuation theory (SFT) in the regime where quantum-mechanical correlations are important (usually at low T). A detailed description of different sorts of SFT is given, including paramagnon theory, local spin-fluctuation (LSF) theory, the Fermi liquid theoretic (FLT) approach and functional integration techniques. It is shown how each of these theories can be applied to various physical systems, including 3He (normal and superfluid), metals, alloys and impurity systems, with the emphasis on the structure of the theories rather than how they have actually been applied. Briefer discussions are given of 'polarisation potential' theories, Gutzwiller theory and renormalisation group methods. A critique of the relative strengths and weaknesses of the various SFTs, and of the information they actually provide about spin fluctuations, is then given. Finally, some areas of current excitement are reviewed, namely the theory of two-dimensional Fermi systems, spin-polarised Fermi systems and 'heavy fermions'.