Dynamic Critical Behaviors of Pseudospin-Phonon Coupled System

Abstract

The expressions for correlation functions in pseudospin-phonon coupled system are obtained. Making use of them, the dynamic critical behaviors of the coupled system are studied theoretically for both cases that the spin ordering triggers the softening of phonon and its inverse case, in which the emphasis is placed on the coupling between pseudospin and phonon. The temperature variations of the poles on the complex plane which determine excitation modes of the system and the spectra of the correlation functions are calculated. As a result, it turns out that the strength of the coupling becomes important as the transition temperature is approached. In the case that the phonon softening causes the ordering of spin, the spectra of the phonon-phonon correlation functions in slow relaxation develop triple peaks corresponding to a relaxational central peak and two resonant phonon side peaks whose frequency shows critical softening.