Dynamics of the strong anisotropic three-dimensional Ising model in a transverse field

The dynamics of the three-dimensional anisotropic spin-½ 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${\mathrm{O}}_4$.