Critical fluctuations in the weakly anharmonic crystal model of a structural phase transition

The criteria for the existence of a central peak in the spectral density of the soft optical mode, in a weakly anharmonic crystal model of a piezoelectric-ferroelectric are examined. We investigate the effects of the critical fluctuations of the optic mode on the internal relaxation process believed responsible for the appearance of a central peak, the relaxation to local equilibrium of the acoustic phonons. The critical fluctuations induce a diffusion in momentum space of the acoustic phonons, leading to an increase in the effective relaxation frequency of the acoustic-phonon distribution function, and a critical increase in the acoustic-phonon linewidth. The increase in relaxation frequency is not sufficient to eliminate the distinct central peak, however, and we conclude that the model will always exhibit a central peak if the anharmonic coupling coefficients are sufficiently small. © 1976 The American Physical Society.