G. G. Guzmán-Verri, C. M. Varma
Relaxor ferroelectrics, a typical example of which is PbMg$_{1/3}$Nb$_{2/3}$O$_3$ (PMN), a perovskite in which the Mg$^{2+}$ and Nb$^{5+}$ randomly occupy the octahedrally coordinated site, have a very high dielectric constant for a very wide region in temperature and have no ferroelectric transition except in applied electric fields. They are technologically important materials for transducers and ceramic capacitors in the electronic industries and also present an interesting physics problem. Cowley et al. in a detailed review of relaxor ferroelectrics have commented that although they were first synthesized over fifty years ago and their properties have been well explored, a satisfactory theory explaining their properties has not yet been formulated. We construct a minimal model for relaxor ferroelectrics based on Onsager's results on models with dipolar interactions, and the short-range displacive transition model with which pure ferroelectrics were understood, together with quenched disorder. We formulate the simplest necessary approximate solution of the model with which each the macroscopic properties and recently measured correlation functions and their inter-relationship are understood in terms of a small number of parameters in the model. Specifically, we calculate and compare with experiments the structure factor as a function of temperature and quantify the various regimes in the dielectric constant of relaxors, the Curie-Weiss regime above the Burns temperature $T_B$, and the growth of unusual correlations recently discovered by neutron diffuse scattering between $T_B$ and the temperature $T_{\max}$ where the dielectric constant is maximum.
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http://arxiv.org/abs/1212.3402
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