Abstract
The dynamics of the Iongitudinal (i.e., parrallel to the $z$ axis) spin fluctuations of the three-dimensional Ising model in a transverse field, $H=\ensuremath{-}\ensuremath{\Gamma}\ensuremath{\Sigma}{i}^{}{S}_{i}^{x}\ensuremath{-}(\frac{1}{2})\ensuremath{\Sigma}{\mathrm{ij}}^{}{J}_{\mathrm{ij}}{S}_{i}^{z}{S}_{j}^{z}$, is studied. An approximate expression for the relaxation shape function is given which gives a simple but realistic view of the dynamics for the entire temperature range ${T}_{c}<T<\ensuremath{\infty}$. Plots of the shape function are obtained and analyzed.
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