The relaxation of a model system of interacting dipoles

We consider a simple model system of interacting dipoles which can be either free to rotate or trapped, and in which the rotation of a dipole can change the state of neighboring dipoles from trapped to free or vice versa, with probabilities that ensure that the fraction of dipoles that are free remains constant, as is required for systems in dynamic equilibrium. The system was studied in a mean field approximation and also by computer simulations. The results show that the non-exponential decay of the system's response function, and hence of its relaxation function, is associated with the fact that initially the decay is due mainly to the depolarization of the free dipoles, while the later stages are associated with the freeing of the polarized dipoles that were trapped and their subsequent depolarization. This process could be a quite general mechanism for non-exponential dielectric relaxation.