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The critical dynamical behavior of the pseudospin-phonon coupled system has been investigated in connection with the structural phase transition of molecular crystals. Based on Onsager's equation of motion, explicit expressions for three correlation functions, spin-spin correlation, phonon-phonon correlation and spin-phonon correlation, are obtained. It has been shown that the characteristic of the spectra of these correlation functions shows wide variation depending on the values of two parameters: The ratio of the relaxation rate of reorientational motion of an isolated spin and the frequency of the phonon, and the ratio of the interaction parameter of direct spin-spin coupling and that of spin-phonon coupling. Especially, in `fast relaxation case', the spectrum of phonon-phonon correlation shows critical softening, whereas, in `show relaxation case' the spectrum gives `triple peak' structure and only the central (relaxational) mode shows critical slowing down leaving phonon side peaks unchanged.
Yamada et al. (Fri,) studied this question.