Dynamics of relaxor ferroelectrics

We study a dynamic model of relaxor ferroelectrics based on the spherical random-bond—random-field model and the Langevin equations of motion. The solution to these equations is obtained in the long-time limit where the system reaches an equilibrium state in the presence of random local electric fields. The complex dynamic linear and third-order nonlinear susceptibilities ${\chi }_1(\omega )$ and ${\chi }_3(\omega )$, respectively, are calculated as functions of frequency and temperature. In analogy with the static case, the dynamic model predicts a narrow frequency dependent peak in ${\chi }_3(T,\omega )$, which mimics a transition into a glass-like state.