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The dielectric response in relaxor ferroelectrics is analyzed in theframework a model for the polarization dynamics in the presence of polarclusters. We associate the origin of polar clusters with the atoms displacedfrom their centro-symmerical positions even above $T_c$. Their collectivehopping in multi-well potentials induced by disorder is analogous with thesituation in glasses. The theory explicitly takes into account the distributionof cluster reorientation frequencies and the effect of cluster-clusterinteractions in highly polarizable crystals, which we describe in terms of thelocal field distribution function. The dielectric constant is obtained from anintegral master equation for the polarization dynamics in the presence of atime dependent electric field. The theory is applied for the analysis of theshape of the frequency dependent permittivity in the typical relaxorferrolectrics $PST$ as a function of temperature. The comparison of the theorywith experiment shows that in contrast to earlier assumptions, the observedVogel-Fulcher dependence of the permittivity maximum is a consequence of theVogel-Fulcher temperature dependence of the cluster reorientation frequency.

Dynamics of interacting clusters and dielectric response in relaxor ferroelectrics