After a brief introduction with a discussion of the concept of the correlation function needed for the formulation of the problem, a progress report is given concerning our knowledge of microdynamic processes in liquids covering the fields of neutron scattering, IR-absorption and lightscattering, dielectric and nuclear magnetic relaxation as well as studies of diffusion and electric conductance. 1. Einleitung wie Ladung, magnetisches Moment etc. zugeordnet sind: die Massenpunkte mIissen ,,beziffert" sein gemiin ihrer Position im Periodensystem (siehe Abb. 1). Jeder Massenpunkt hat einen Ort ri und eine Geschwindigkeit ui = dri/dt als Augenblickswert. Das mikroskopische Augenblicksbild einer FWsigkeit k8nnen wir als ein System vieler Massenpunkte im Raum ansehen, denen je nach Umstiinden weitere physikalische Eigenschaften Ber. Bunsenges. Phys. Chem. 85, 992-lo05 (1981) -0 Verlag Chemie GmbH, D-6940 Weinheim, 1981.

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An introduction is given to the methods and results of some recent researches into statistical thermodynamics bearing upon the correlation functions of magnetic moments in Heisenberg-coupled spin-only magnets, and their intimate connection with neutron-scattering theory and practice is brought out. T h e interrelationships between the correlation function, the relaxation function, the generalized susceptibility, the power spectrum of the fluctuations and the neutron scattering are explained, and it is shown that insights into any one of these aspects can serve to illuminate the others. Different forms of approximate theory are seen to be suitable in approaching the topic through these different avenues ; the method of moments for analysing the power spectrum and the connection with Green function theory are described in particular. Some examples are calculated in molecular-field theory and with various other simple approximations ; expressions for the frequency spectrum of the susceptibility are obtained in various temperature ranges. T h e extreme forms of the frequency spectrum in appropriate conditions as a set of delta functions, as a pseudo-Gaussian and as a pseudo-Lorentzian are derived, and the transitions between these cases are considered. The approximation of spin diffusion and its limitations are analysed; the problem of the dynamical slowing-down of magnetic fluctuations near the phase-transition point is examined and the current position in this enquiry is set out.