Dynamical behaviors of magnetic systems near the critical points in the nonhydrodynamical regime are considered. For this purpose we construct a kinetic equation to describe the time evolution of critical fluctuations that corresponds in a sense to the Boltzmann equation of dilute gases. A graphical technique is developed to deduce the self-consistent equation for time-correlation functions of critical fluctuations from this kinetic equation, and the properties of the time-correlation functions of spin fluctuations for the Heisenberg isotropic and planar ferro- and isotropic antiferromagnets are discussed. The results are then applied to the high-frequency sound attenuation in magnetic systems.
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Kyozi Kawasaki (1970) studied this question.
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