Central-peak and soft-mode dynamics of K${\mathrm{H}}_2$P${\mathrm{O}}_4$-type ferroelectrics above $T_c$

Building upon a recent work of Tommet and Huber, we have studied the effects of the range and the anisotropy of the interaction forces on the dynamics of a three-dimensional Ising model in a transverse tunneling field. The procedure makes use of a truncated-continued-fraction expansion of the longitudinal-relaxation shape function which, by comparison with an exact computer experiment, has recently been shown to yield good results. Our results show that with increasing anisotropy the central peak becomes narrower and the soft mode broader. Close to $T_c$ this effect may become very large. Upon proceeding from the Brillouin-zone center to the Brillouin-zone boundary, the width of the central peak may increase several orders of magnitude while, in striking contrast, the frequency and damping of the soft mode would undergo only minor changes. At the same distance from $T_c$ the central peak of a deuterated system may be four to five orders of magnitude narrower than in an undeuterated system whereas the changes in the soft-mode spectra are much smaller.