Modeling of polar clusters in disordered perovskites: the S-K model with tunneling

The polar clusters generated by random non-central impurities in quantum pa raelectrics determine to a great extent the complex dielectric behaviour ob served in systems like SCT, KTN or KTL. The competition between a quantum p araelectric phase and an impurity-driven ferroelectric or glass phase depen ds on the concentration and on the nature of the interaction between cluste rs. This work presents a simple model in which each cluster is represented by a quantum two level system involving an effective Ising dipolar moment e ta and a tunneling energy A. The interactions between clusters are taken in to account by following the guide-lines of the Sherrington-Kirkpatrick mode l for spin glasses. General expressions for the polarization (P) and the Ed wards-Anderson order parameter (q) are given and the phase diagram involvin g temperature, the normalized mean interaction energy J(0)/J and tunneling energy A/J(0) is built.