Griffiths phase manifestation in disordered dielectrics

We predict the existence of a Griffiths phase in dielectrics with a concentrational crossover between dipole glass (electric analog of spin glass) and ferroelectricity. Particular representatives of the above substances are KTaO₃:Li, Nb, Na, or relaxor ferroelectrics like Pb_1–xLa_xZr_0.65Ti_0.35O₃. Since this phase exists above the ferroelectric phase-transition temperature (but below that temperature for ordered substances), we call it a “para-glass phase”. We assert that the difference between paraelectric and para-glass phases in the above substances is the existence of clusters (inherent to the “ordinary” Griffiths phase of Ising magnets) of correlated dipoles. We show that randomness plays a decisive role in the Griffiths (para-glass) phase formation: this phase does not exist in a mean field approximation. To investigate the Griffiths phase properties, we calculate the density of Yang-Lee (YL) zeros in the partition function and find that it has “tails” inherent to the Griffiths phase in the above temperature interval. We perform calculations on the basis of our self-consistent equation for the long-range order parameter in an external electric field. This equation has been derived in the framework of the random field theory. The latter automatically incorporates both short-range (due to indirect interaction via transverse optical phonons of the host lattice) and long-range (ordinary dipole-dipole) interactions between impurity dipoles, so that the problem of long-range interaction considerations does not appear in it. Received 17 May 2000