Dynamical Aspect of Magnetic Critical Phenomena

Abstract

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.