Soft modes in two- and eight-direction order-disorder ferroelectrics

The soft modes in the twoand eight-direction order-disorder ferroelectrics are calculated under the mean-field approximation. We find that the conventional method of the pseudospin model to calculate the soft-mode frequency is incorrect, and present a valid modified method. It is demonstrated that the conventional method does not show the soft-mode frequency going to zero at a critical temperature in the presence of random internal fields, while the frequency calculated by our modified method goes to zero in random fields at a critical temperature. In the eight-direction ferroelectrics, the soft-mode frequency decreases to zero at the first-order phase transition temperature though the symmetry has been destroyed at high temperatures under an ex-