New Kind of Phase Transition in Randomly Distributed Tunneling Dipoles in Alkali Halides

We show that very dilute concentrations of dipole impurities distributed in alkali halides (for example, ${\mathrm{OH}}^{-}$ impurities in KCl) undergo a phase transition provided that the average impurity-impurity interaction is greater than the tunnel-splitting energy of a single dipole. This theory predicts a temperature-dependent cusp in the dielectric constant. The polarization in the absence of an applied field is predicted to be zero even below the transition temperature.