Application of Green's function method to the study of order-disorder ferroelectrics

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Abstract
In this paper, our work which was performed on order-disorder ferroelectrics by the Green's function method is reviewed. First, the Bose Green's function method is modified by introducing three undetermined constants to make the method self-consistent. If the constants are not introduced, the method would give a contradictory result. Then we apply this method to the transverse Ising model with four-spin coupling to study the properties of phase transitions of order-disorder ferroelectrics. A new condition to determine the transition temperature Tc and the discontinuity at the transition temperature (S z)C has been found. We have also determined the critical values of the model parameters, beyond which the transition is first order. Finally, a comparison of our results with the experimental data of PbHPO4 and PbDPO4 indicates that our method is more suitable for describing PbHPO4-type crystals, and can give a quantitative explanation.