Abstract
The dynamics of the three-dimensional anisotropic spin-\textonehalf{} Ising model in a transverse field is studied above ${T}_{c}$ by a method in which the coupled-chain problem is reduced to that of a single chain in an effective field. The problem of a single chain is studied by means of Mori's continued-fraction expansion in a four-pole approximation. The moments are obtained by using the time-dependent correlation function calculated in the $c$-cyclic and in the improved $c$-cyclic approximations [J. Phys. A 13, 223 (1980)]. A comparison between these two approximations is done by calculating the critical temperature as function of the tunneling field. The one-dimensional correlation length is obtained, and it agrees well with the experimental results for the quasi-one-dimensional ferroelectric Cs${\mathrm{D}}_{2}$P${\mathrm{O}}_{4}$.
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